The one article you can have an effect on is article 4, since it symmetrically bounds the two of you to inspect each other's living spaces. That would let Argos come to the hotel to inspect it if he pleases. The game carries on regardless of what article you contested (or if you just signed the contract right away), but Argos will notice if you spotted his loophole and there might be some shenanigans later if you didn't.
I think it is article 5, since I think that mean either one broken the contract, the Mirror will revert to Foreman, which means he have the chance to break up everything even you do not done anything worng.
