When I first got Poképark Wii, I thought Sharpedo evolved into Wailord because they both lived in the Beach Zone and Wailord was after Sharpedo in the Poképark Pad.
And I only got the idea of "hey, maybe I shouldn't teach HMs to my main team" a month ago. Thankfully, I took Dive, Waterfall, and Fly off my Latias long before that.
Edit: Oh, yes, I also thought that N was a girl the first time I saw a picture of him. Got robbed of that delusion soon enough.
Edit #2: Forgot some stuff and didn't want to have three posts out of ten, so...
When I found my first ever shiny, a Machop, I used Leech Seed on it. Thankfully, I caught it before it died.
I used to be mildly scared of Super Training and Pokémon-Amie. I really need to re-EV train my Latias...
Until very recently, I thought Psychic resisted Fairy.
Also used to think that Suicune was Ice-type. Well, it makes more sense than it being Water...and it matches up with the legendary birds...oh, who am I kidding?
One that's also fairly recent: I was playing Y, training somewhere, and the Pokémon I was battling put my Pyroar to sleep. So I tried to wake her up with a Berry, but it didn't work. I kept on using Berries, until eventually she woke up on her own. It was only after the battle that I realized... I was using Aspear Berries, rather than the Chesto Berries I should have been using.
This one wasn't me, but...once I was playing Y while my sister was watching. I encountered a female Hippopotas on Route 9, and my sister asked, "Is that shiny?"
I still pronounce a lot of Pokémon names "incorrectly", because I just can't process the apparently correct pronunciations. However, I no longer pronounce Gyarados "Guy-air-uh-dos" or Drifblim "Dribflim".