First, I am addicted to hatching pets and getting that "perfect" one. It's so fun!
My one suggestion came up because I found myself wasting precious energy on silly mistakes. I usually have a pet I'm training and a pet I use while playing the game. Often times, especially once the pet gets close to Epic, I forget to switch the pets out and train the wrong pet.
It would be wonderful if a picture + the name of your pet appeared on the screen for each pet game where you select the "world" you're playing in (and therefore which skills will be trained).
I would be willing to bet I'm not the only person who has made this mistake! Fellow wizards, please give your feedback on this idea!