This is just the thing - the exterior isn't the issue. You have soldiers whose first and worst enemy is boredom. You're not going to order them to stand idly by waiting for the stormcloaks to come and attack. You're going to keep them busy doing the most pointless things you can to keep them occupied. It's all about discipline. The Thalmor and the Legion (who are both meant to be well organised military wise) would encourage discipline in their soldiers, and so part of that is that they would spend some time making the fort exceptionally clean. Cobwebs in the corners wouldn't have any excuse to be there.
Have you ever gone to a US military base? I believe that they spend the first hour of the day cleaning until the place is LITERALLY spotless.
Besides that, your reasoning doesn't make sense to me. It takes less than five seconds to right an upturned table so that it can be used to eat off, for sake of example.
I don't think the Thalmor are bored, in fact they're quite busy hunting and torturing civilians. Cowebs are the least of their worries. Also, please don't compare a modern day American base to a medieval fort. Seriously.
And if you absolutely have to, have the decency to compare with one in a war theatre (like Northwatch keep). I guarantee you that American bases in France and Germany during WWII and bases in Vietnam during the conflict of the same name had "cowebs" in corners, and worse things. I'm sure the forts in Summerset Isles are cleaner, like army bases in the US are cleaner.
Finally, it looks to me like Northwatch Keep is just an abandonned fort recently taken over by the Thalmor as a base of operations for their torture missions. I don't think they've been there for ages...