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".

Lee Novak put the Spireites ahead, nodding in Gboly Ariyibi's cross, for his 14th goal of the season before Adam Hammill's deflected equaliser.
Jamal Campbell-Ryce was dismissed for two yellow cards, one for kicking the ball away, but Ollie Banks side-footed home to restore Chesterfield's lead.
Hamill then hit the post as Barnsley could not find a late leveller.
Defeat in their first league game since winning the Johnstone's Paint Trophy means Barnsley are now six points off the League One play-off positions.
Chesterfield, meanwhile, have now opened up a four-point gap between themselves and the relegation places.

The finds were made by a team from Durham University, which is surveying the site on Midland Road before it is redeveloped for houses.
The remains are believed to date to the medieval period, but could be Roman.
Developers Westleigh plan to build 70 homes on Midland Road once the archaeologists complete their dig.
Dr Rebecca Casa-Hatton, lead archaeologist at Peterborough City Council, said: "At the moment we presume they may be medieval but we can't discount they may be late-Roman.
"It's very, very crowded so the cemetery would have been extensive."
She added archaeologists were expecting to find human remains in this area because of similar late Roman or medieval burials uncovered during the building of the railway line during the 19th Century.
"Hopefully, this excavation will shed light on the period of these burials and the burials found in the general area," she said.
Gary Turner, head of investment and partnership at Westleigh, said: "The discovery was made about six weeks ago and since then we have obtained a licence from the Ministry of Justice to exhume the remains.
"Once removed, the remains will be analysed to unlock further details on their history."

A bomb exploded after being thrown at Coalisland police station on 26 March 1997.
The 37-year-old man has been charged with causing an explosion.
He is due to appear at Dungannon Magistrates' Court on Wednesday.
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.
[NEXT_CONCEPT]
Ten-man Chesterfield edged out Barnsley to boost their own survival chances and dent their hosts' play-off ambitions.
[NEXT_CONCEPT]
About 70 human skeletons have been uncovered by archaeologists during a dig at a former factory in Peterborough.
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A man has been charged over a bomb attack on a County Tyrone police station 18 years ago.