Hi Dopers!
Geez…my thread has morphed into a monster while I was away…
Okay, here’s the Straight Dope, such as I have. 
When I went into work today, Jeff was there, and had been informed of the situation; he was bitter about the whole thing, but he said, “Well, if the guy comes back for it tonight, I guess I’ll give it to him, but if he doesn’t come back by the end of my shift, it’s so mine!”
The thing is…guilty gulp there’s more than one bar where I work, and I didn’t work at Jeff’s service-bar tonight…so I don’t know if the guy came back or not. I was in a totally different bar in another area of the building.
However, I am inclined to think he didn’t, b/c it was very quiet again tonight, and the other bartender who did work in Jeff’s area said he heard nothing about it. Nor did the (different) manager mention anything about it to me, and I’m positive he would have, just b/c this sort of thing obviously doesn’t happen very often. (And this is a manager who, based on previous experience, would have almost certainly solved the problem immediately had he been present…unlike Chris the other night, whose middle name is Pass The Buck.)
But I won’t know for sure until tomorrow night when I go back to work. wince I know, it’s awful, I started this thread and then went to work tonight and mentioned it to Jeff…got his viewpoint for you all…and then totally spaced the follow-up til I got home because I worked another bar.
However, it is established that Jeff was willing to give the guy his money back, if the guy came back for it tonight. Whether the guy did or not, I don’t know yet…but I’m pretty sure I would’ve heard if he had, b/c gossip is the lifeline of any restaurant. 
I do apologize for not being positive, though. I hope you don’t all think I really suck. I swear I’ll find out tomorrow for sure!
As for the moral and ethical side of it, which is obviously a hotly debated issue…
Tipping is kind of separate, in my opinion, from other questions of this nature; the intention of any tipper who says “Here is your tip” is, by default, to give the waiter/bartender whatever that tip amount is. Regardless of how huge/small it is. This is a transaction that’s not cut-and-dried; it’s not like working a till, where X amount is required and expected, and anything that deviates is obviously an error on somebody’s part.
I’ve gotten stiffed, I’ve gotten horrible tips, I’ve gotten average tips, and I’ve gotten incredible tips. I never assume that any of them were a mistake; to me, it’s part of the job I took, and I always assume that people give me the tip they intended me to have.
The problem with saying that somebody can take back a tip is that if they can, why can’t everybody else? I’ve gotten tips from some pretty intoxicated people before, and the tips were probably a lot more than they’d have been if the people were sober. Does that mean that they can come back later, when they’ve sobered up, and tell me they made a mistake and want their money back? Does it make it wrong for me to even take such a tip, knowing that they’ve had a six-pack and that they’re feeling more generous than they normally would? Am I stealing from them? Should I tell people not to tip me an unusually large amount, in case they regret it later? What about people who are drunk and forget to tip me at all? Should I assume they meant to, and remind them? Or should I just assume they didn’t want to tip me? It works both ways.
You see where I’m going.
A tip is mine the moment you give it to me, plain and simple. I have no control over what you give me, so I’m going to assume you know what you’re doing, whether it’s a great or a horrible tip. Otherwise there’s room there for you to come back and want your money back, or room for me to “explain” to you that you made a mistake and probably meant to tip me more than you did. That won’t work!
Which is why I say the money belongs to Jeff. Because Jeff, like the rest of us, assumes that what is handed to us as a tip is what was intended to be ours. And I don’t think it’s fair to assume there’s a gray area there…b/c otherwise Jeff also has the right to pipe up and say, “Hey man, you must’ve made a mistake. You only tipped me ten percent.” How pissed off would customers be if we said that! And to me it works both ways. A really bad tip is never assumed to be a mistake, so why should a really big one automatically be under suspicion?
That’s my logic, anyway. You can argue about the morality of taking advantage of the customer’s obvious mistake, but the fact remains that all waiters operate under the assumption that whatever they get is what they were meant to have. And to turn that back around on the waiter, and try to work out some kind of deal where a tip can be debated later because he was supposed to “know” that a mistake was made, just isn’t fair. Otherwise any tip is up for debate, and can be called a “mistake” later and have to be given back. “I didn’t double-check what I gave you” is, IMO, no different from “I was drunk” or “I realized I didn’t have cab fare when I left the bar” or “that tip put me over my credit card balance and I didn’t realize it” or any other number of reasons you could give to get your money back. That’s not how it works; none of those things are within my power to control. I don’t get to assume you made a mistake if you tip very poorly, and ask you to correct it, so why should I have to assume you made a mistake if you tip very well, and offer to correct that for you? A tip is a totally discretionary amount of money, so ordinary rules about the exchange of money for goods don’t apply because there is no set price tag attached to service.
My $.02, anyway.
FWIW, the karma attached to giving the guy his money back is worth mentioning…but that’s a whole other issue. The guy’s right to get his money back is what we’re debating.