Well, since we're talking about weird bugs, I've encountered a game-breaking one in Chapter 5 that has stopped my progress. Apparently the game doesn't like it when the HiPriest (playing the part of Thieves) raid the towns. As soon as they move onto the door-tile on the towns and start raiding the game locks up. Maybe it's got something to do with playing the HiPriest's map-animation? Not sure how to fix this one - seems like a job for someone well-versed in the ins and outs of FE4 - so I'm kinda leaving it alone for now.
Other Non-Game-Breaking glitches:
Also, I think making Sylvia anything but a dancer broke the "Dance" scene more than it was already broken. I tried saving and reloading several times to get Sylvia's dance to play (She's currently a Sniper) but her sprite just disappears and it just locks up and plays the song forever.
Another weird one on Chapter 4, the Level 4 arena enemy was an AxArmor with a "Hero" axe. However, when we got into a fight, what would happen is he would play the Throwing Axe animation, but the axe would be invisible. Then, hit or miss, the screen would go dark for a moment, and the enemy would disappear, and then my counterattack would whiff, and my character would just stand there like an idiot forever and ever. Even pressing B to try to cancel the fight did nothing. When I tried the Bow-Arena course, it was the same sort of thing, except it was a Warrior with an invisible bow (I forget what bow it was). The only way to get past level 4 Arena would be to use characters who could double-attack for enough damage to kill him before he counter attacked. This was before I changed the Armor-mountain-movement cost so I'm stumped. Lamia actually did the same thing (Had an invisible weapon and then disappeared) but my character could hit and kill her, so it wasn't a problem then. Not game breaking, but it did screw me out of a lot of Arena abuse.
Also, not a bug per-se, but the wyvern riders between me and Lord Byron were so strong that they instagib him immediately before I can even get up there. Not game-breaking, but unfortunate. I wanted to see what nonsense holy weapon he hands me :( (And then the game breaks because HiPriests don't like capturing towns or something, so it became moot)