LikeMM wrote:One more problem.

If a song is playing and I quit MM near the end of the song and restart MM, let MM finish the song -> The play counter does not get updated. Looks like it needs a fresh play duration to be reached to consider it as 'played'.

Ok, That's right. It needs a fresh play duration to be reached to consider it as 'played'

I see the same: http://www.ventismedia.com/mantis/view.php?id=12414

One more problem.

If a song is playing and I quit MM near the end of the song and restart MM, let MM finish the song -> The play counter does not get updated. Looks like it needs a fresh play duration to be reached to consider it as 'played'.

Try this:
Bring up 'File Properties' of a song when it is playing. Make some edit to the comments or any other property. Don't close the window yet.
Let the song finish. You will see play count and last played columns in 'Now Playing' get updated correctly.
Now okay the changes you made. The play count and last played will get reset to previous values, forgetting the latest play occurrence.

MM 4.1.5.1711