Because there has been such an obvious hint that there will be a real, full-out, war in the hp-universe, the use of apparition in this war should be expected in most hp-fanfics with a plot.
The main objection towards using it is obviously the 'pop.' That is, if it makes a sound when you apparate to a place where hostiles are present, they will know you are there and curse you instinctively. I have seen this solved in a few fanfics by making the main character (almost exclusively Harry) able to apparate in silence. While this solves the problem, I, personally, don't like it since not even Dumbledore can do that. I have no objection to making your character strong and talented, but there should be limits and this particular problem can be solved in other ways.
For example: If you make a sort of silencing spell on the area you wish to apparate to, or temporary deafen the nearby occupants, they will not hear the 'pop' and as a result won't greet your arrival with a curse that you may have problem ducking. Now, I know there are several flaws in this solution, but they are not unsolvable. First, if you cast magic in the immediate area of other wizards they should be able to feel it, especially if you cast that magic on them. While I agree that this is a problem, unless these wizards are highly trained they should not be able to determine exactly what this spell does. If you instead wish to agree with my first assessment that Harry shouldn't be invincible and therefore shouldn't be able to cast spells over great distances, you can just use this solution when he apparates to closer locations. The other side of a door or wall, for example. If you instead wish to make the opponents a bit more talented and insist that they should be able to feel magic cast in their proximity and react in a way that takes the surprise out of the attack, there are solutions to this problem too.
One solution could be that you cast some form of silencing spell on yourself before you apparate, with the intentions of muting a sound that does, after all, come from you. This one can only be possible if you approach the logic of magic from a certain view. You could argue that the sound doesn't really come from you but from the air rushing out to make room for your sudden arrival. My solution to this is that you simply cast an aura of silencing that will include the area that the air rushes to once you've appeared (on a side note about the air, if you slowly create a void of vacuum in the area you intend to apparate to there should be no sound when you appear). These solutions assumes that you can keep spells activated while apparating. If you decide that this isn't possible then I have no solution to offer except portkeys (which must be pre-set on location, or not if you wish to change that) or maybe some sort of temporal fireplace, or maybe hacking into an existing one. But now I'm reaching for straws.
Another side on apparating would be using 'splinching' as an advantage. For example splinching an eye to a locations to see what is there (or an ear, or nose, or hand with a wand, you get the idea.) This poses a whole new set of problems. First, if you splinch your eye, how will you get it back? Could you apparate the rest of your body to that exact location and make it fit? I feel the need to limit exactly what you can do here. You should decide on which part is you and only be able to apparate one of the two parts to the other. I, personally, can't see an eye being conscious enough to apparate anywhere. But then again, with this logic you shouldn't even see through that eye, so maybe I'm being stupid. The second problem is this: does the eye float or just fall to the ground? What would happen if someone touched it? And what about apparating just part of the eye, or just the lens? Could you still see? Because logically, the smaller part that appears in thin air, the smaller the 'pop.'
If these ideas seem too much for you, or just plain bad, then I would suggest creating a magical item and somehow transport that to the place you wish to spy on. Speaking of items, if you apparate somewhere your wand and clothes will go with you, so why not splinch an item? And if you really want to twist the magical logic in a funny way you could just splinch your glasses and see through them.
If none of these solutions fit your idea then at least I've pointed you in the right direction. Which is this:
Nothing is impossible or not allowed. However, it could be a good idea to make boundaries and rules to add credibility to your story, or just to avoid confusion. When you've created a limitation in your story there is no reason why you shouldn't work around it. In fact, not doing this would be boring at best.
This has been an encouragement to others and a way for me to run ideas through other people. Any and all of these ideas are open for you to use.
Don't assume and don't stick to one way of thinking, open your mind.