Incorrect handling between time signatures and BPM
The PLAY function in MuseScore is not calculating time correctly. It seems to be using the quarter note as the basis for all timing.
If a song starts in 4/4 at 60 bpm, the the quarter note should be 1 second in duration. But if you change to 3/2 time, then the half note should become the unit of measure and it should also be 1 second in duration. MuseScore seems to treat the 3/2 signature as if it were 6/4 meter. In fact, if the opening time signature is 3/2, and the tempo is 60 bpm, it treats the half note as 2 seconds in duration instead of 1 second as it should be.
Here is a good explanation of how to handle changing time signatures in a song. Please see http://www.musicarrangers.com/star-theory/t15.htm.