Until a recent fix, a large number of enemies would result in some being off screen. The fix to shift off screen enemies to the left introduced this overlap bug but it doesn't really hinder gameplay. I don't think it is due to the rapier.
The auto bug is old and separate (I assume). To manually prevent this, don't finish a battle by killing an enemy in auto/end turn. Kill the last enemy manually and the next battle should be fine. I tried to track this bug down but I suspect it involves the UI.