...yeah, they definitely skipped a lot of details.
So much so that at first I thought this was just a "what if" montage playing in his head.
But well, if the author didn't do that, there'd be a lot of questions to answer they apparently didn't want to bother with.
If the MC was suspected for being unemployed they could have easily found out that he had employment until the very day before.
There should be no evidence linking him to the crimes. With his earlier report the culprit forging some would raise suspicion.
If the police force is corrupt, how can that be with the skill system setup as it is?
Are there no people in the judicial system with a skill that'd allow them to determine his innocence?
Are we to assume that the serial rapes just stop at this point, because it'd be quite strange were they to continue with the alleged rapist locked away?
What kinda garbage tier piece of shit is that god? ("I want a skill to make my family happy." "Oh sure, here, take this unprecedented, but very specific skill without any explanation on how it works. I'm sure it'll be fine pffft...")
All these open and very obvious problems (at least at this point) don't make me hopeful for this story's future.