It would be most unwise to play it and WIN, this would give them every excuse to void the winnings.
If the amount is small, it would be reasonable to keep it as a bonus (many times I have had a bonus added, but no E-mail telling me why).
If the casino has a decent cashcheck facility, it should be possible to find out where the funds came from. With MG, it is PLAYCHECK that you need to look at to track a bonus, select the relevant session, and apply the game filter to show a game you have not played, then select "detail" - this should show the bonus. Some MG casinos have a bug, where the filter is lost when you select "detail".
If the amount is large, and pretty obviously a mistake, I doubt you could get away with playing it, although if you lost it, you could just uninstall the casino rather than have them deduct it from your next deposit (as many will do).
The biggest mistake I have experienced was when I had a Neteller timeout. I complained to CS, and was not happy to be told it would take till after the weekend (I wanted to play a promotion). They managed to credit the 2000, and I played, however, at the end of the weekend ANOTHER 2000 appeared. It took THREE attempts to convince CS is wasn't mine, and when I did manage, they said it could take 48 hours to fix, but in the meantime I could play, and they would deduct the 2000 from my balance. I didn't play, as I didn't want to risk losing it & having my next deposits owing to the casino. I got 100 for my honesty
I have read here of a player at
32Red who had over 1000 credited twice in error as a withdrawal, and 32Red let them keep it
(Which made them look a bit silly, as they had given 32Red a public roasting on the forum over it).