I've got a few, but sadly no videos.
Fallout New Vegas: Every now and then, my companion would go sprinting into the distance as if to say "The spell is broken, I'm free, I'm free!" only to return a few in-game hours later as if nothing had happened. Wierd.
Dead Rising: "Oh, you're trying to save my worthless life? Good, while you do that, I'll crawl into this crowd of friendly-looking zombies, maybe stand in the wayt when you're fighting a boss."
Saint's row 1: When driving, your enemy knows not what the brakes are for, it seems every single time there was a car chase, my prey sped up like they were going for warp speed, only slowing down when they crashed into something... which means if they never crash, you may be in for frustrating mission, enemy gang cars never giving you a much peace to catch up to suicidal fuckwit de jour. (final rollerz mission, for example)
MineCraft: Not that I expect genius from farm animals, but I think FIRE is something they wouldn't casually stumble into. I don't know how many have perished in my burning netherrock fences and lava well, but I've watched the stupid fuckers jump into the fire/lava when it was a block above stumbling level. They aren't just blindly walking about, they actually hop up to their deaths. I get free cooked steaks just by visiting the bridge I lined with fire.