I used to feel that I ought to let people off mouse slips and vice versa - but these things do tend to balance out, so I don't ask for them back and no-one asks me.
Mouse Slips
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It's happened to me a couple of times, but in 10 min live chess, so just had to put up with it.
I'd be ok with rectifying any obvious 'mouseslips' though; wouldn't want to win otherwise.
I think it just comes down to personal preference.
I prefer not to for a couple of reasons.
Firstly, I think like OTB where if you touch a piece and are allowed a takeback, you must move that same piece, that should be the rule online also.
(I've given them in the past, only for the opp to move a completely different piece, obviously not a mouseslip in the first place then....)
And also because a lot of the time I notice that I get the most requests for takebacks when the move could easily have been a genuine blunder too.
Even top GMs make stupid blunders.
Stupidity should not be allowed to be taken back! 
I did one of them in a game. I was about to smother-mate him when my rook fell too short, where it could be taken. This gave him having a superior position so I resigned.
Seeing that thread again, I can report that the "fear of mouse slip" issue did resolve nicely for me as I decided to not go into Live Chess. In turn based you can adjust your settings such that you move and then still have to press "submit". :)
This was my worst mouse slip. The guy was kind enough to offer me a draw (no takebacks allowed). I accepted, and now never use a track pad to play... nuff said.
At least I'm not the only one to make a mouse slip in that position. They say that's the only way NN can win.
When it's obvious like post 8 I offer a takeback... or in that specific game I would just resign as white lol.
In a series of games, if they're an interesting opponent and hang a piece not due to a slip but a super obvious blunder, I'll offer a takeback then too.
It's interesting, sometimes they have their pride and decline the takeback and resign :)
rather to avoid finger slip becuase it may leads to wrong piece selection :D
I find the most of my "mouse-slips" occur when I click and hold a piece over a destination square waiting for my opponent to move. If they made a move I wasn't expecting or I decide to move a different piece, I usually right-click to quickly put the piece I'm holding back. Sometimes this doesn't work however, and instead the piece I'm currently holding gets placed on the square I was hovering over.
Nobody's fault but my own for being lazy!
I don't understand why the mouse slips. It almost seems that someone else has control as it only happens when it is a critical move. I might just hang it up. I recall long time ago it was the battery but not this time around.
I just experienced my first "mouse slip" (or rather "touchpad slip"). Luckily, it was just in the tactics trainer, but it still made me cringe. I think I would never dare claim a mouseslip in a game myself, but I guess I would probably let my opponent take back a move if it seems obvious that his rook/bishop/queen en voyage "fell down" at an obviously silly square. What do you think?