So I encountered my first big (and kinda funny bug) in LH.  I had one of my heroes use the command that allows another unit to immediately take a turn (forget the actual name, sorry).  Instead of the unit taking the turn, my hero got to go again, then again, and again, and again.....until i ran around the map killing every last enemy.  Now that is some overpowered glitch .

After that I checked on my research, and some of the titles of the different techs wouldn't scroll with the screen.  The titles just hung out in space while I scrolled through the other techs.