Tap on your pet. After that a menu pops out with the following: Scratch, Sit, Play Dead (don't know about that), Follow, Hide (yes, hide the pet).
Maybe train?
And also the pet should be able to show moods every time you use the glove button on them.
Pets should be able to find items while walking like:
[Insert pet name here] has found x1 donuts!
Also being able to name the pet and re-name it.
Your pet should walk in the back of you (just like pokemom heartgold and soulsilver)
Oh! and your pet should have a bar (just like the bar that shows your gangster or a cop) but shows their happiness level from 1-100. (this will also show after using the glove button on your pet.
That's it. Hope you like some of my ideas!!