To add to the list, supposedly dream world pokemon can't be shiny. However generated dream world shinnies passed through bank. Also I'm unsure if dream world pokemon are restricted to dream balls, but they were also passed in premier balls. I was unable to pass dream radar or "hatched" pokemon in premiers.
ITT: Haha, I'm such a rebel! I'll blatantly ignore that fact that it's the hackers fault Gamefreak even had to implent a hack check in the first place. Haha, you suck Gamefreak, but I'll buy your games anyway.
Here's a pic of a Timid Eruption Heatran. Heatran can only get Eruption in a Pokemon Ranger event, and it is always a Quiet nature. It works with other nature locked events, like Aura Sphere Raikou and Air Slash Suicune.
I did this with the Raikou, it passed but couldn't make it in online matches.