This isn't the most absurd example but it's an interesting AI oversight that I've never encountered before. I'm doing a mono-Steel run of X and while training a Nosepass in the Battle Chateau I battled two Viscountesses with Scary Face Axew and Cotton Spore Swirlix. I'm used to 'good' AI trainers using Speed-lowering moves until they confirm that they're faster than you, but because I was using Thunder Wave then spamming Rock Tomb, I was still faster than them even after Nosepass went to -6. Still, they continued to try and lower Nosepass's Speed. I was underlevelled, so it took another 4 or 5 turns to finish each battle and both opponents just kept spamming an ineffective Scary Face/Cotton Spore until they fainted.
Ordinarily, 'don't use ineffective moves unless you're forced to' is one of the first AI flags set for NPC trainers to distinguish them from wild mons, but it seems that the 'try to lower your opponent's Speed if they're faster than you' flag overrides that? It might not work the way I'm supposing, but I found it kinda interesting and silly.
EDIT: Aliana's Mightyena behaves the exact same way lol