Two bugs I encountered in the same battle, presented in the form of a story:
One day Boris was descending a staircase as part of his weight carrying regimen. He reached the bottom of the staircase and proceeded out a nearby doorway. At some point, he noticed that his shadow disappeared. And his firearm. And he could no longer see himself in reflections of nearby windows.
Confused, Boris sat there and looked around for a bit. Was he really invisible? Suddenly, he heard a teammate screaming in the distance.
"HOSTILE! HOOOSSSTILE!" yelled the soldier.
Boris ran to where the shouting was coming from and found his eccentric friend Nicolai pointing at a nearby pile of rubble.
Everyone was standing around, looking confused. A few people took pot shots at the rubble, which didn't seem to do anything. Explosives didn't seem to do anything as well. Everybody seemed to think Nicolai had lost it until one bored soldier discovered that she could shoot through a wall, accidentally killing the rubble in the process. "Wow," said Boris, "what an anticlimactic ending." "Who said that!" exclaimed Nicolai, who's uncanny ability to see living rubble did not allow him to spot his invisible friend.
OK, story time's done, back to business. Both bugs occurred during the same scout mission. The first bug I couldn't find reported anywhere. I'm not sure what caused it and haven't been able reproduce it reliably since. Boris did descend a flight of stairs (seen to the right of the first image) and exited through a doorway in one turn, but I don't think he disappeared until after the turn was done. Also, he was being used as a test subject while trying to reproduce the weight stats bug (hence all the ammunition he's carrying). If I had to guess, it's probably a race condition issue which occurs when ascending or descending stairs.
The second bug has been reported already I think; there was an alien hiding in a spot where he should not have been able to get to, and as a result could not be seen. I figured I'd include it anyways because both happened within a few turns of each other, and it made a good story.