I see no problem in checking if the wallet has any coins. I would have checked. If it was empty, I wouldn't bother trying to find who it belongs to. And hopefully, the real owner wouldn't deposit any bitcoins on it without realizing it is gone. If it was funded, then I would try to find the owner in a few different ways.   
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Yeah, I know a lot of users would be comfortable with that, and I'm not saying it's wrong for them to do that. I just personally wouldn't be comfortable doing that. It's almost sticking my noses into someone else's business, without having any sort of right to do so. It's hard because if you find it on a beach or a secluded area, you basically have no one to contact or give it too, and like I said even the act of giving it to someone could potentially compromise it. That's why I like the moral dilemma, it's very similar to the train track dilemma, basically whatever you do or don't do has some sort of consequence.

If it was at an event, you'd normally just give it to the event organisers, but you're kind of relying on them to be trustworthy themselves, which you can't always do. Handing it to the Police is probably your best bet, but I know a lot of users would be uncomfortable with that also.