Dean knew his dog which he was reasonably certain was a dog, as after carefully running his hands over the creature, he'd determined that Max was indeed furry and dog shaped, wasn't normal. What invisible dog is? But, after the creature had saved him from the Hoodoo practitioner's girlfriend who'd shown up with a shotgun, and helped him aid in the post-Katrina clean-up of New Orleans which had been halted by Hurricane Rita which had re-flooded the Ninth Ward when he decided to stay behind and help out for a while, he'd decided that despite Max's little allergy to salt and iron, it wasn't evil and that killing it would just be mean.
He couldn't get the sound that poor dog had made the time he'd tested the creature by sprinkling salt on it out of his head, especially after the hurt and whining creature came up to him and hesitantly licked his hand afterward and forgave him. He knew that he should probably get rid of Max, but he found himself thinking It isn't hurting anybody every time his hand reached for the salt or the iron crow-bar he kept for ghosts. Unlike the ghosts he'd whacked any number of times, Max was solid, and very real. Each night as he crawled into bed, he could feel the large furry creature curl up next to him like the dog Dad had never gotten him and Sam no matter how many times they - mostly Sam - had begged.
As for the contracts he'd also won off of the man-witch that he'd won Max from, he'd released the poor slobs who'd sold their souls for cash, love, fame, and in seven incidences, to cure a relative of a deadly disease. He didn't need people's souls, and wouldn't know what to do with them if he got them anyway. He didn't even want to know why that man-witch was going around collecting souls anyway.
The fifty grand was shut in the trunk along with the weapons, and would be going towards the Dean Winchester Hunting Fund. He'd need that fifty grand since his dad had disappeared, and finding him or finding out what had happened to him would likely be a difficult undertaking. The potential difficulty of the search for his dad was why he was headed to Stanford to get Sam despite the fact that his brother had told him to get lost when he'd tried to drag his brother on a hunt after he'd finished his freshman year a little over two years ago.
That whole incident had been an unmitigated disaster which he'd rather forget, and had been why he'd never approached or even tried to talk to Sam in the two years since. He still checked to make sure that Sam was still alive every once in a while though.
As he drove to Palo Alto, Max sat in the back chowing down on a hamburger. The creature wouldn't touch the dry dog food he'd bought, but would eat meat if he gave it to him. Max preferred it raw but would eat burgers in a pinch. He briefly wondered how Sammy would react to his new pet, considering...
The first thing Sam said when he hopped into the car in order to head to Jericho, California where their dad had been when he'd last contacted Dean was "Dean, your dog is fugly."