A man lodged a complaint with the Police Ombudsman's Office for NI after the incident last year.
He said he had been wrongfully arrested and that his home had been unlawfully searched.
The man said his wife was "hysterical" at finding police in the garden.
He was taken inside his house and arrested in connection with a firearms offence which had happened the previous day, before being taken into custody at a police station.
The man was later released when police realised he was not the person they were looking for.
When a Police Ombudsman investigator examined police files, he found that the issue lay with an incorrectly recorded date of birth in a handover information pack provided to the officer who organised the search.
The officer who compiled the pack had recorded the name and address of another man of the same name, but had mistakenly added the complainant's date of birth.
The officer who co-ordinated the search said she had checked the details in the handover pack, but found no-one of that name living at the address.
She then searched for a more up-to-date address using the complainant's name and date of birth, which resulted in his arrest and home being searched.
The officer who recorded the wrong date of birth admitted his mistake and "apologised to the complainant and his family for the upset and annoyance which resulted".
It said police "later tracked down the right man, who was subsequently arrested".
The Police Ombudsman investigator said "the mistake had unfortunate consequences for the man and his family".
They said they had "recommended that the officer should receive a disciplinary sanction, and that has since been imposed by the police".
A police officer has been disciplined over a mistake which led to armed police being sent to the wrong address during a search of a family home in County Down.