In the meantime he flew out with his wife Cathy, 57, and Faye and John's eldest child Ava.
He said: "I had filled in the first five forms all correctly, but it was taking some time.
"I had no idea I had made a mistake on the baby's form until Harvey's travel was refused to the USA.
"I couldn't believe that they couldn't see it was a genuine mistake and that a 3-month-old baby would be no harm to anyone.
"Harvey was even summoned down for an interview to the US Embassy. I really couldn't believe it.
"I went down with him and his mum and took him in for the interview, but he can't even speak as he's so young.
"We went down on the Monday and flew on the Thursday, but sadly the Visa didn't come in time, so half of us went and baby Harvey came a couple of days later with his parents and the whole sorry business cost me an extra £3000."
He added: "It was a very expensive mistake, but I was hoping the US Embassy would realise that it was just a simple error without us having to jump through all the hoops.
"If you are a terrorist -I suspect you'd not be ticking YES on the ESTA form anyway."
The ESTA question that Paul inadvertently ticked Yes on by mistake asks: "Do you seek to engage in or have you ever engaged in terrorist activities, espionage, sabotage, or genocide?"
He went on: "Baby Harvey was good as gold for the interview and never cried once - I thought about taking him along in an orange jumpsuit, but thought better of it.
"They didn't appear to have a sense of humour over it at all and couldn't see the funny side.
"He's obviously never engaged in genocide, or espionage, but he has sabotaged quite a few nappies in his time though I didn't tell them that at the US Embassy."
All eligible international travellers who wish to go to the United States under the Visa Waiver programme must apply for authorisation under the Electronic System for Travel Authorisation.
- Originally published in Telegraph UK