Well, besides all the prima facie evidence of being the worst edit warrior ever.
If they are edit warring using sockpuppets it may not be possible to spot that they are doing so. If someone became suspicious that something odd was going on with a particular article and ran a checkuser on all the contributors the best they could find is that lots of people are using TOR, but if we allow people to use TOR then it is quite a leap to assume that it is just one person using TOR. The same can be said about people editing from the same city, or same ISP, of course, but I would imagine the abuse rate on TOR is higher than for any ISP or city by virtue of the fact that any vandal can choose to use TOR, you don't have the same choice with where you live, so the situation is going to arise more often with TOR than it does otherwise.