Pokemon that have stats passed their base stats and hacked abilities. Those pokemon will not make it on Wifi. They will either be turned into bad eggs if their stats are hacked up or just will not be allowed on wifi.
However you can still battle your friends on your friend code list. Provided none of your pokemon have over the base stat of 510. If they are they will turn into bad eggs. You can have hacked moves to battle friends, but those won't be allowed on Wifi either. Anything that is not legit will not fly in Wifi.
Trainer: NIKO
Pokemon B/W Friend Code:
3783-4062-8709