I don't think MC has a problem. The approach is just different than in winamp. MC considers you've listened to a song once you've listened to it, that is when you're done playing the full file.
Almost correct. Actuallly MC adds the play count if the track was played over 50%.
BTW, there's a problem (this time) I see with this approach: when MC fails to play a file (e.g. because your soundcard doesn't support the sampling rate you've chosen in de DSP) the playcount still increases for the files you've failed to play. Trying to fix my DSP configuration I ended up having some files "played" like 20 times although I couldn't listen to them. Is there a way to edit the playcount manually to fix this? I don't want to reset the playcount to 0, I'd like to set it to whatever figure I'd like.
You could reset the play count and quickly advance the track a few times.
You should always make a new library backup immediately if you suspect a problem. Make a library restore after the problem is solved. That will restore the play counts too.
I make library backups all the time. I keep about the ten latest available. If MC hangs I always make a restore after restarting. Sometimes the library gets corrupted if MC was saving library files.