plaza items and potatoe heads' outfit question

i know that you can scroll over in the main area to the blue tent next to mouse trap to see how many potatoe head outfits you need, but is there any way to check on the mascots, statues, and building parts?

No easy way that I can tell other than just looking. No idea how to check on the mascots (other than you'll have the achievement "Plaza Party" if you do; they're hard to see but I suppose you can look around the park to see if you have them all) but I can tell you what else to look for:

Gold statues: Pretty obvious if you have these; just look for the gold statue in front of each of the building.

Building Parts:
Life: Moneybags sign, hot air balloons, inflatable people
Twister: Balloons, laser lights
Mousetrap: Con-trap-tion, giant cat statue, fireworks
Yahtzee Hands Down: Cards sign, laser lights
Clue: Cards sign, thunder and lightning, question mark garden
Plaza overall (last thing you get, after you have everything else): Tickertape

Usually have to finish each game about 6 or 7 times to get all this (original or remix, full game or quick game; doesn't matter; and you just have to finish, not win). Basically over the course of getting all the other achievements you'll play them enough times to get all this anyway. Hope this helps. Good luck!

BTW to unlock all statues, mascots, building parts, and Potato Head costumes you need to complete (just finish, don't need to win; and can be either original or remix, full game or quick game):

Life & Mousetrap: 7 games each
Clue, Yahtzee Hands Down, and Twister: 6 games each