So he gets frustrated that it turns out even if he hadn't signed the marriage registration form, nobody would've been harmed, but I don't really see why he should feel that way. I mean, for one thing, he didn't know nobody would be harmed when he decided to sign the form, so he took the best decision he could given the information he had available to him at the time.
Secondly, it's revealed Kuchinashi 'knew' that it was fake and could've told him as much, in which case he could've avoided signing the form, which added to his frustration, but again, why? If it was up to Kuchinashi, she could've just not demanded he sign the form in the first place, so obviously she will never do anything that reduces the chance of him signing the form.
Also, even if she revealed that it was probably fake, what, is he gonna risk not signing the form? The clue is that the numbers turned upside down reads "LIE", how the fuck is that sufficient evidence to let a bomb go off in a public theater? Like, what if it's just a fucking coincidence? Clearly, he would still need to try to find and disarm the bomb ahead of time to be on the safe side, so he'd still need to sign it.
In conclusion, it's better to just not worry about things you have no control over.