When you're removing a snap that's posted across multiple tribes, what happens? Does it only get removed in your specific tribe?

Yes. It will no longer appear in your tribe but will still appear in the others.

In addition, I read somewhere that removing comments is going to be a headache as moderators across different tribes will have different standards/rules regarding what is appropriate.

I can see why. I presume that the comment would no longer appear if viewed from your tribe but would still appear for others. I can imagine this would have to be handled through property tags on the back end, but I certainly wouldn't want to be doing the programming.

What do you guys think of this?

I have no complaint, since the site is free. And I really don't have a comment other than what I've already observed. If they can make it work then they deserve all the things. :)