They ended the episode with a threat we already know will not be carried out. There's a technical term for this: Anti-climax.
By the way, on the issue of contrivances, the chances that no one found out about the money being given away are zero. Jesse should have had any number of people offering him matches in hopes he tips really, really well.
Another by the way, Lydia is a Walter White too. Why is she treated differently?
Another by the way, Walter is not even tempted to stray sexually, not even after Skylar cheats. Jesse has been a monogamous, caring partner with only two women. The writers have been very careful not to taint the antihero and the antivillain with any distasteful sexual sins, as opposed to cool violence.
Well.. if the cops would analyze the money bundles they would find Jesse's fingerprints on them.. game over. He can't explain where the money came from and even if the cops wouldn't be able to charge him for something (i guess it isn't illegal to throw money around) the IRS would sure love to talk to Jesse about the money given that he had no registered job for the last few years, if ever.
I don't see Lydia being treated any differently, she's just a way more cowardly Walter White version and after the shootout in the desert has at least as much to answer for as Walter (doesn't matter that "only" some drug dealers were killed).