Alright. So. I feel a TAD BIT silly asking this, but here goes nothing. I was wondering what, exactly, the Blue Building is. Like, what happens when you get in? Also, how do you improve the overall rating of your pet/know the overall rating of your pet?

We're not allowed to tell you what the Blue Building is or what it does ;)

The overall rating of your pet is all its battle stats combined, not including intelligence. You improve it by training your pets at the gym over in the Riverside Valley or using stat-boosting items (that tend to be expensive)

Ah, gotcha. Thanks much!

We CANNOT discuss whats inside the Blue Building. The pet rating, pertaining to the Blue Building, refers to Level, Health, Defense, Strength. You can improve those in the Training Center in Riverside Valley.