On gamecube games, the holes cut out in the plastic cases sometimes cause the cover art insert to be pushed in causing creases. Is there any good way to flatten or iron the paper to smooth it out?

You could try. I've ironed boxes with parchment paper, and it makes a huge difference.

Ive done this with parchment paper and a t-shirt press my wife has. Comes out beautiful. The only thing I would say though is don't do it directly on the spine while folded or completely open... I made that mistake the first time and turned it into a hard crease that didn't want to open. T.T

Can you guys please give step by step directions for this? I don't want to mess up.

I use a t-shirt press and parchment paper to flatten things too. Here's probably 100x more information than you'll ever need on the topic.
http://www.kaptainmyke.com/comics...

Book press or t-shirt press. You use heat with a bit of water, or just press it as-is. I can read that article, but I'd like to know how you guys do and your personal experience. I've considered looking for a book press if I could get a decent one locally for under $100. I wouldn't mind an antique one because I like old stuff, so long as it works properly.