Nope, I wouldn't grant it, I wouldn't ask for it, and I wouldn't accept it if it was offered.
Mouse slips

Use the other way of moving pieces - click on the piece and then on the square you want it to move at. No mouse slips possible.

Use the other way of moving pieces - click on the piece and then on the square you want it to move at. No mouse slips possible.
Hmm. I would think that a slip would be even more likely using that method. If you're moving a pawn forward, for instance, and you're moving quickly, and you click as you're moving your mouse. . . I don't know, it seems like it would be easy to move your mouse too far without realizing it, when at least you'd see it if you drag-and-drop.
I'll have to try moving that way and see how it feels.
Rich

Mouse slip-ups are definitely part of the game. I've come close a few times in the heat of a 15-minute game when I'm moving a piece and suddenly run my mouse off the pad, but I manage to keep the left-click button pressed down. I also find myself moving pieces to squares I'm unsure of, and when I decide against the move, I find the best thing to do is move the piece directly over my opponent's king, which returns it to its original square.
I have had mouseslips before however i have also had players use it as a tool to avoid a loss.I had a game where he played for the mate shop an missed i had a trick shot which won for me.I told him after the game i did not buy the mouse slip as he took about 30 sec for the move when he had about 55 sec on his clock in a 5 min blitz game.Now i have allowed takeback if i find it to me a true mouseslip an not a blunder.

I almost always will grant a takeback request, especially if it's a mouse slip. My goal is to practice for "real games" where, by the way, take backs are never given or requested If they think they see a better move I want to know what it is. If they've been a real arse through the game though, running at the mouth the way you sometimes see online, then I'd rather get the game over with as quickly as possible in which case the more mouse slips they make the better lol.
If a takeback wasn't an option (like here) I wouldn't accept a draw. Again this is how I look at the games, they aren't the real serious ones, if you want to start over then resign, I'll be more than happy to do a rematch, if you want to play with the mistake as it is then keep playing.
Funny enough, sometimes you grant take backs and they end up making a worse move (or one at least I think it worse). If they use it to get the time back on their clock then I'll reject the offer. Sometimes they catch on that I accept them and I had one guy use almost all his time then request a take back... I don't think so lol.

I made a mouse slip the other day in the opening I played g5 instead of g6, my opponent gave me the draw but I was rated over 200 points higher so I'm sure he didn't mind.

Don't be fooled eighter, since in quick live games, offering draws and even "mouse-slips" is used by some players to create uncertainity, and to make the opponent spend valuable time. I would advice people to play on in case of a mouse slip, and to reject draw offers if they want to play on. In case of wanting to draw themselves, take the draw.
I you want to prepare yourself for OTB or serious chess, never get involved in discussions like this in an ongoing game. In a friendly and unrated game, you do as you like of course, but my advice in any rated game, is play on or take the draw, no matter of mouse slips, draw offers or whatever. Follow the rules, beheave like a nice person, but it is a war game, and the goal is to put his king in mate within the given time. It is not a competition in etiquette.
It seems to me that mouse slips are part of the game in an online world, but I thought I'd see if anyone has any other thoughts, since the chess.com live interface doesn't have any sort of "request takeback" button (when I used to play at Yahoo! games, I usually granted the takeback).
Say you're playing and your opponent, who has played well so far, puts a piece in harm's way with no support. Within seconds, your opponent types, "Damn, mouse slip!" in the chat window. Given the play so far, and the fact that you would have moved the same piece just one square farther, you're fairly certain that it really was a mouse slip.
Now your opponent offers a draw. Do you accept? Would ratings matter in your decision?
I've had opponents claim mouse slips several times, and I know I've slipped on a move a couple of times myself. Recently, someone actually claimed two in one game -- and given his rating and level of play in the game to that point (as well as in the rematch), I believe him. But nobody has ever offered a draw in that situation.
I doubt that I'd grant it, since I really consider it part of the game online, just like touching a piece is usually part of the game live. But I thought I'd see what others think about it.
Thanks,
Rich