Being a little pedantic, but it's important to be clear, your son touched in at Amersham. Because he then made a journey from Marylebone to Paddington the system has automatically added the extra touch to make the full journey. This is however definitive proof that he did pay for the whole journey via TfL, even if he wasn't aware of it. Chiltern would be very brave to continue prosecuting this when faced with this evidence.
You say he touched his debit card on the gates at Marylebone NR and they didn't open. I think this is unlikely unless the gate had trouble reading the card. The contactless system will always let a card exit to avoid someone being trapped inside. You might want to consider exactly what you say about this. The fact that the card continued to work means that if it had read properly at Marylebone NR then it would have opened the gates.
Although technically he failed to show a valid ticket when asked, he had actually paid for the journey, so I would hope that Chiltern will be magnanimous and drop that case.
At least your son now knows he can use PAYG on National Rail, and if he does have a forces Railcard and uses trains regularly in London off-peak then I would recommend getting an Oyster card and adding the discount.
Thank you for your comments. I know 100% the card reader didn't work for the trainline ticket which is why he went to the ticket office but I'd better try an clarify about the debit card, if I can, which I doubt, so it may be best to remove that point especially if I end up replying on his behalf.
I am hoping they will reconsider. I presume the occasional person is able buy their ticket at the office just before the gate for whatever reason, so the fact he bought a train line ticket before he reached the gates, should also be acceptable although I know now that a purchase should legally be before he steps on the train.
The bit that gets me is the Inspector says he challenged my lad. So he went to a random person to ask if he had a ticket? No way. You can't get through the barrier without a ticket. My son phoned me after - because he went to the office to say his ticket didn't work then got accused of not even being at Amersham and he was pretty cross. Doubt he mentioned checking the CCTV in his report, because he very obviously didn't.
With regards to the other two offences - I think they've printed off 3 months of travel and decided he always gets the train from Great Missenden hence the short ticket. By tapping out at Amersham, at least it's proof he travels from both places. I've got a stack of evidence for this and he also travels back to Chesham but that's not often.
He will be definitely be getting an Oyster card, that's for sure!