Currently the two training activities I've seen are running around and doing a front flip. Maybe add some additional variety, such as come, sit, stay, roll over, lie down, shake, beg, heel, play catch, etc? These shouldn't be too difficult to add, since they don't require graphics.
Also, I noticed that another user had a bird, but it still said "ran around". Maybe the list of training texts could be specific to the type of animal?