Disclaimer: I have noted the ideas that are entirely mine in order to avoid sullying the invented languages that Mr Tolkien was kind enough to share with us.
The error in the password on the West Door remains a curiosity for students of the Ring War. The Elves of Eregion had no difficulty with it, in part because they knew the password, and in part because they had adopted their lord's peculiar grammar and incorporated it into the dialect of Eregion. (At least, this was so among the Fëanorians and craftsfolk with whom Celebrimbor had the most contact - it appears that the Sindar and many of the Noldor retained the more conventional usage of Celeborn and Galadriel.)
One can only suppose that, following the rules of Quenya grammar, in which the accusative case is not inflected, Celebrimbor did not realise that a noun following a verb is to be lenited in Sindarin. Like his father and grandfather, he had a gift for language, and he spoke Khuzdûl quite well, even writing some texts regarding the grammar of the language that are still considered to be authoritative by the Dwarves themselves. However, it also appears that he was indifferent to Sindarin, and by his indifference, may have inadvertently given Khazad-dûm its unflattering moniker, 'Moria'...
He was carving the design into the polished oak table when Ambarto finally arrived. Next to him, his father held up his hands in helpless resignation. Tyelperinquar had an idea, and no paper or quill on him.
Maitimo redirected his glare toward Ambarto; he had even less patience for tardiness than he had for wanton destruction of his furniture. "Now that we are all here-" he began.
"I assume that this is about the ban," Tyelkormo broke in.
"I told you Angaráto could not be trusted," Carnistir said darkly.
"Certainly not after you attacked him," Maitimo said. "But in any case, Singollo was bound to hear it sooner or later.
"I have heard from Nolofinwë and Findaráto," he continued. "As they have many Sindar in their lands, Sindarin has already become the language of common use."
Curufinwë laughed. "Surely, you do not expect us to honour the ban?"
"Of course not. Still, we must respect it in our dealings with the Sindar and with our cousins. They will not make an enemy of Singollo."
"He has been looking for an excuse," Makalaurë said. "Some of the younger folk in Doriath have been learning Quenya, and I had a letter this summer from Daeron. It seems that he had composed some songs in Quenya that were not well received by his king. I have received nothing more from Daeron...I suppose I should not expect it, now..." he trailed off.
"Yes, that is our secret plan - to turn his people in to Quenya-speaking thralls," Curufinwë laughed.
"You have been quiet, Ambaru-...Ambarto. Have you any thoughts?"
"Our brother has gone native," Tyelkormo laughed. "He speaks nothing but Nandorin these days."
Ambarto smiled faintly. "It is true that Quenya is not spoken in my lands. I do not see why I am here."
"So, does the ban extend to the Tengwar?" Carnistir asked. "Shall we start writing to our cousins in cirth?"
"Evidently not, as the letters I have received are written in the usual script."
Curufinwë rolled his eyes. "Fool! Does he not realise that our father invented the Tengwar?"
Tyelperinquar completed a last loop of the design and looked up to find the hall deserted.
Or nearly so. Ambarto was watching him. As Tyelperinquar sheathed his knife, Ambarto left his seat. "May I?"
He nodded, and moved to let his father's brother examine his work.
"Gauntlet?"
"Yes, that is what I was thinking. It would be too heavy for a bracelet."
"Would you make that for me? It would suit me, I think. It makes me think of vines and leaves."
"Yes, of course." Tyelperinquar stood. "Er, did I miss anything of importance?"
Ambarto studied him for a moment, his head cocked to the side. "I think," he said, "you might want to learn Sindarin."
When they first set up camp in by the lake, the area seemed deserted, for the Sindar of the North were a shadowy people, well-hidden in the caves of the Ered Mithrim, which they left only at necessity. One might stare at a rock face for several minutes before distinguishing the Elf standing before it in his misty grey cloak. They communicated, at first, mostly in gestures, but the Mithrim nonetheless made their disapproval clear: the Exiles were entirely too bold, too noisy and would soon attract unwanted attention. Fëanáro was unable to do more than note phoneme changes in Ilkorin before the 'unwanted attention' attacked.
Curufinwë dismissed the language - he thought it a lazy tongue with a degraded phonology. Yet, he had at last the opportunity to do something his father had not already done before him. Thus, he resolved to know Sindarin so well as to become not only its master among the Noldor, but so learned in its subtleties as to be an authority to native speakers.
This, Tyelperinquar could not understand. How could one master a thing that fell though the hands like water? In Aman as in Beleriand, gold would always melt at the same temperature; nickel would form predictable alloys with other metals. The laws of the elements were timeless, immovable.
Sindarin was liquid, changeable. He could not count on it to retain the same rules from one day to the next, from one place to another. His difficulty was not simply one of unruly grammar or uncertain homonyms, however. The Sindar had a wholly different lexicology. A word did not have two meanings - it had both meanings at the same time. In the mind of the Sinda, two concepts linked by language were one and the same. One might hear an elf noted for his 'green' eyesight (laeg) or a particularly verdant shrub described as 'sharp'. To the Sinda, they were both green and sharp. His grandfather would have understood this intuitively, but his father, less imaginative, did not. (1,2)
Sindarin, Tyelperinquar thought, was entirely too much like people, whose actions and reactions so often puzzled him. He did not share his father's talent for manipulating that puzzle into the picture he wanted to see. He therefore dealt with people sparingly and indifferently, assuming that they would understand him as they would. His approach to Sindarin was the same. As Quenya was the language of their house and most of their people, and the only outsiders with whom he dealt were Dwarves, he had little reason to speak Sindarin, in any case.
With Dwarves, of course, he spoke Khuzdûl. Never before had they taught their language to Elves, and Tyelperinquar knew that this was a great honour. It would be unthinkable to treat such a gift with carelessness. Moreover, he understood the Dwarves better than he understood his own people. Their work absorbed them entirely, and if they were gruff or remote, it was simply because their craft was more important. (3)
Like its speakers, Khuzdûl was bedrock solid; Dwarves had neither the inclination nor the audacity to meddle with the language of Mahal, and the usage of Nogrod and Belegost in the First Age remained unchanged in Second Age Khazad-dûm.
In Eregion, Pengolodh viewed his sometimes archaic and sometimes haphazard speech with a mixture of amusement and interest. "I am a scholar, not a grammarian. I cannot simultaneously observe the changes in a language and correct them, can I?"
"My father took a rather different view," Celebrimbor said wryly.
"Yes, I can imagine. In answer to your question, I have done a bit of research-" Pengolodh paused as he sifted through the piles of papers on his desk. "Ah, here it is." He looked up at Celebrimbor. "The treatise on First Age peoples of Eriador that Lord Celeborn wanted. Must set that aside so that I can find it again," he muttered. "Ah - the evolution of elu." He sat down again, somewhat dustier for his efforts.
Celebrimbor smothered the urge to sneeze. His father would be appalled at the disorder. Bits of paper stuck out of pigeonholes, books were upended and lay open under paperweights to mark a passage for future (or long past) research and stacks wobbled on every surface, including most of the floor.
"It is quite simple, really. Elu means 'sky-coloured', which in turn meant 'star-coloured' before the rise of the sun. After the rise of the sun, it took on the meaning of 'soft blue', but it never lost its association with the stars. In Doriath, this was not a problem, as the word for 'sky' became gelu in Doriathrin. Among the Northern Sindar, however, Thingol was sometimes called the 'Blue King'." (4)
"Aquamarine, then," Celebrimbor mused, already designing the tressure in his mind. "Did you know that there is a variety of aquamarine that fades to white when exposed to the sun? It must have been like that, for the Sindar," he mused. "The stars would have appeared to be a brilliant blue, in comparison to anything else, before the moon and the sun."
Pengolodh nodded vigorously. "Some colours would have been easier to discern than others. I think you have hit upon something." He smiled. "Your trouble, Celebrimbor, is not that you do not understand. You understand too well and cannot decide upon the best of all possibilities. Language, like people, is not always logical. You must rely on instinct.
"But, do not worry overmuch," he continued. "No one has ever been killed by bad grammar."
...Celebrimbor's unintentional riddle is of less interest than his use of the word, 'Moria' on the doors. Why would a Dwarf-friend refer to the Hadhodrim's greatest wonder as a 'black pit'? A new work by Master Pengolodh reveals that the error that nearly killed the Fellowship was not the only one in Celebrimbor's inscription.
The common Sindarin word for Khazad-dûm is Hadhodrond. However, in the Second Age, it acquired a second name, used entirely by the Exiles: Boria. The word was a Sindarinized version of Quenya vorë, 'lasting' and ia, 'ever'; together meaning 'Everlasting' and made in honour of Khazad-dûm's long history. The great Dwarf mansion predates the Elves' arrival in Aman, making it the oldest creation in Arda not made by the Ainur.
As Sindarin renders the genitive without a preposition, it must have seemed logical to Celebrimbor that it would be inflected (as it is in Quenya). Thus, 'Boria' became 'Moria' on the West Doors. This was perfectly understood by the Elves of Eregion. However, as their dialect died out and relations between the races became chilly, 'Moria' became an epithet for Khazad-dûm, which few Elves of the Third Age had seen. After the Balrog arose, the name was adopted by many of the Dwarves, for it had truly become a 'black pit'. (Such usage may be seen in Master Frodo's account of the Council of Elrond, in which a doubting Glóin tells of the ill-omened attempt to retake Khazad-dûm.)
General sources:
Most of the Sindarin and Quenya linguistic information comes from Helge Fauskanger's Ardalambion website. Anything that is incorrect is my faulty understanding. Helge Fauskanger is also credited with the observation that pedo mellon a minno is rendered in the vocative rather than the accusative, and that this was the source of Mithrandir's incorrect translation. Had the writing read, pedo vellon a minno, the meaning would have been obvious.
The notion of Boria as the name of Khazad-dûm is entirely invented and the linguistic foundation of the word dubious. To the best of my knowledge, Tolkien never attempted to explain why Celebrimbor used 'Moria' on the West Door.
Notes:
(1) He could not count on it to retain the same rules from one day to the next, from one place to another.
Pengolodh explains that the Elves liked to make innovations to their language, but when changing a sound, they would never change just one word, but all words with that sound. (The Peoples of Middle-earth, 'Dangweth Pengolodh' pp 398-9 pub Houghton Mifflin) That's exactly what happened with þ. However, even before the Exiles reached Endor, Sindarin had 'become the product of unheeded change like the tongues of Men.' (Ibid, p 401)
(2) A word did not have two meanings - it had both meanings at the same time.
The ideas in this paragraph owe much to Through the Language Glass: Why the World Looks Different in Other Languages by Guy Deutscher (pub Metropolitan Books 2010); 'The Colors of Elvish: A Linguistic Exploration' by Fiondil (essay published at The Silmarillion Writers' Guild website); and a third source I can't recall - it may have been a Tumblr post or it might have been an essay.
(3) With Dwarves, of course, he spoke Khuzdûl.
The text only tells us that Curufin learnt Khuzdûl, but I think it's logical that Celebrimbor would also have spoken it, considering his close friendship with the Dwarves of Khazad-dûm. (The Peoples of Middle-earth, 'The Shibboleth of Fëanor' p 358) We can also infer that Pengolodh might have learnt it, as he 'dwelt among the Dwarves of Casarrondo' for some time. (The War of the Jewels, 'Quendi and Eldar' p 397 pub Houghton Mifflin)
(4) Among the Northern Sindar, however, Thingol was sometimes called the 'Blue King'.
This is complete nonsense. Tolkien originally had Elwë glossed under 3EL-, but noted that it should be moved to EL-. (The Lost Road, 'Etymologies' p 400 pub Ballantine/Del Rey)