If your opponent makes an accidental move, e.g. by slipping the mouse, and it is obvious that is was accidental, how should you continue? Should you just play the best move as if your opponent's last move was intentional? Some of my opponents have suggested that I should accept a draw in such situations. Others have asked me to make a dummy move, so that they could undo their last move by moving the piece back to the square where it was before.
FICS has a "takeback" option; other sites may have something similar.
The link gives full details but the idea is that you type
takeback n to request undoing n half-moves. Either player can do this so, if you make a mouse-slip, you can just type
takeback to ask your opponent to undo that move (n=1 is assumed if you don't specify); if your opponent makes a mouseslip, you can still type
takeback to allow them the chance to undo. In the second case, you don't have to wait for your opponent to reply while your clock ticks away: if you make your move, the takeback is modified to
takeback 2 so your opponent has the offer of undoing both his mistake and your reply to it. When offered a takeback, you can either accept or decline; making a move automatically declines. Accepting a takeback also resets the clocks to what they were at the moment when the mouse-slip was made.
On sites where this is not available, I'd recommend not making a dummy move, unless you were already in a losing position. You don't know that your opponent will behave honourably. They might exploit your generosity. I also wouldn't offer a draw unless, perhaps, a draw would have been a reasonable outcome before the mouse-slip. If your opponent was already losing, why should they gain half a point just by making a mouse-slip?
Mouse slips are a result of moving too fast.
Why should your opponent have the advantage of moving fast, without suffering the disadvantage of slipping once in a while? So in blitz I wouldn't accept any takebacks, it's just part of the game.
Of course in longer time controls you could show more leniency ...
If my opponent makes a mouse slip, I either offer a draw or continue with the best available move. It depends a bit on my mood. If I make a mouse slip, I just continue as usual and don't expect any favors in return. I can add that using a "click, click" method instead of drag and drop decreases the risk of mouse slips.
There is no 'right' answer to this. Personally, my rule is that I never give takebacks and I never ask for them. If I make a mouseslip then I'll live with it and if I come up against someone who whines or complains because I won't give a takeback then I'll add them to my no-play list.
It's probably no accident that this attitude seems to be more common the higher up the rating lists you go.