Now that I think about it, Bowser should've kidnapped and left Isle Delfino, so Mario either obeys Isle Delfino and stays detained and Peach remains kidnapped or Mario has to break the law again to rescue Peach. Bowser's plot does depend on Isle Delfino actually enforcing it, but just imagine the legal conundrum that'll give Mario that'll make Bowser cackle with joy.
Yeah, the Pianta Police should have detained him as they want to ask questions surrounding the vandalism of a figure of a similar silhouette (Mario matches the description of the wanted guy). However, if they ran an ID check, Mario clearly has no criminal history or warrants (unless they filed out an arrest warrant on the very little details they have on very terrible visual and witness testimonies), and in fact, Mario is a well-known celebrity in Mushroom Kingdom known for being heroic. Freaking hell, Mario just took down a goopy Piranha Plant right when he arrived, so there ARE witnesses already who can defend for Mario being innocent. Additionally, later on, Shadow Mario messes around with the denizens, and surely...they would have seen Mario chase after the doppleganger and then realize something is up...but at that point of the story, the whole imprisonment subplot for Mario is forgotten. Honestly, after getting entangled in the cluster---- law system that is Isle Delfino, I wonder why the hell Mario still wants to vacation there after all.
Another question that I wish was answered is if Isle Delfino is even part of Mushroom Kingdom. Yeah, they may have exotics but that doesn't necessarily mean that it's not owned by Mushroom Kingdom in a similar vein of how the US owns Hawaii and subject to its laws. This is when our headcanon runs into play hahaha.
Then again, Mushroom Kingdom sends out an entire police fleet running after two morons who vandalized a scoreboard in a stadium and did nothing when a stadium gets blown up by a huge explosion, but at least they noticed who actually was responsible and chased the right people.
Meanwhile, Diamond City Police gets their entire fleet taken out by soccer balls.