As to the question in the title - nothing I'm aware of. But ask me again in a month or so - I was thinking of dropping it out again to see.
I shouldn't be surprised if I had problems, as I've been told that as a baby milk would sometimes make me sick. However, I don't seem to find any difference currently with or without it.
It's difficult to know, because problems with your stomach as a baby could be down to cereals, since one of the first things mothers used to be told to give children was "baby cereal". I'm told I couldn't take orange juice either - again a strong recommendation at the time. My mother went to the doctor and he told her to give me rosehip syrup instead. I was fine on that. I guess it could well have actually been gluten screwing with my stomach causing problems with other foods - at the bottom of it all, so to speak.
I'm pretty sure I'm not good on grains. I've never had an allergy test, but I feel awfully bad if I have a beer or two - and it's not just the alcohol! Beer will also give me a sneezing fit, as will porridge. Bread has made me literally throw up on occasion. None of these effects is invariable for me, but they seem like definite reactions.
I sort of think that dairy may be in there in the Paleo "package" not because of its inherent qualities but because it makes a tidy package. We know prehistoric man didn't eat grain (rather didn't eat much grain - some did gather some), and we know he didn't eat dairy products. Voila! You have your "narrative". It's persuasive, of course, because: (a) farmers tend to be shorter than hunters (not invariably but on the whole); (b) they're rather less healthy; (c) we know some people do have definite allergic reactions to both foods mentioned.
But because it all makes a tidy narrative doesn't make it definitively true. Problems with milk could be down to other factors. If someone definitively does have problems with milk, maybe it's down to the fact that it's pasteurized, or that it's from A1 cows ...
Besides, we know of herding cultures that seem to be very healthy - and certainly no shorter than people living by the chase. Stefansson - who didn't know one was supposed to abhor dairy - pointed to the skeletons of mediaeval Icelanders (who were herders) as an indication that "animal food" made you healthy and robust, whereas cereals didn't. interestingly, he says the skull shape is in some ways not unlike that of Eskimos - which suggests that such things are not only determined by genetics but by what we eat.
Robb does sometimes speak of lectins being present in milk. On the other hand, they're there in nuts, too ... which are, nevertheless, in the Paleo Diet, owing to the fact that prehistoric people gathered them.
So I don't know - try dropping it out for a month or two and then "challenging" yourself with some. If you want to be rigorous you have to omit butter, too, because it has some dairy proteins in it. Use olive oil, coconut oil, goose fat, or whatever instead.