Adam joining Five-Zero really was absurd. Aside from his long criminal history (even though he's portrayed to be a "good bad guy"), he had zero law enforcement experience, and honestly would have been more useful as an undercover collaborator than a full-fledged member of the team.

They just ran out of ideas regarding what to do with him, so they dropped him in there as a team member, and now suddenly he's the one operating the supercomputer because Jerry left the show.

Also, they really bungled that plotline with that young female ex-con he was guiding into setting up some gangster. Remember that whole thing? It started out with potential, but then totally went off the rails, with Adam inexplicably caring about her way too much (yet without any kind of romantic/sexual element to it), and then the girl unceremoniously died off-camera.

Now they never speak of it again.

Like the restaurant plotline, they just decided to abandon that whole mess and are pretending it never happened.