Tournament rules for RftG, how to ensure fair play?
You could discard cards face down in-front of yourself, splayed out so that a count can easily be made, before discarding the cards to the common discard pile. Alternately, until the next reshuffle, you could place those cards face down under the development/planet (splayed slightly) that they are paying. This would give players a much longer time to verify that they didn't cheat.

I am not exactly sure how someone would keep extra cards from an explore. During the explore phase, don't you keep either 2 cards of 3 (normally, without any development/planet bonuses) or if you explore deep you keep 1 of 7 cards. How exactly is someone keeping extra cards from this? Are they merging their hand and their Explore, or keeping them in different hands?