Others have already mentioned the National Insurance number hole, and the Coronation Street address hole. And there's the overwhelming, 'why on earth would John shoot himself in the foot like this anyway?', hole. He's risking his own and Fiz's liberty.
Is John, with his Keats obsession, his uni. education and his PG teaching diploma that he keeps banging on about, so dreadfully, mind-numbingly thick, that he really, truly believes that using a fake ID to teach along the road in Rochdale or Barnsley is a foolproof plan? Give us a break. For one thing, it's hardly any distance away, and for another, teachers have to attend training days and conferences, etc.. He MUST know that he will inevitably be spotted. What are you going to do John? Grow a massive Fishwick-style 'tache, and wear sunglasses? How about a balaclava? Better to do a TEFL course and try Outer Mongolia, John.
Also, before he even gets NEAR the Rochdale/Barnsley stage, isn't it likely that Fishwick will notice that all his personal papers have been half-inched, and just maybe report it to the cops?
Personally, I don't think that John IS thick. I don't tend to think he's pushing the old self destruct button, either. No. I think it is blindingly obvious that he has a serious personality disorder. He seems to tick all the boxes for the diagnosis "aggressive narcissist". Plus, his eyes have developed a creepy, disturbing glint behind those specs. Things can only get worse.
Maybe a way forward for his character would be for him to go into therapy? After he's nicked, that is. Whatever - Fiz and Chesney need to get out of there, fast.