It would be nice to watch Zero Dark Thirty in the cinema in Pakistan. The extraordinary final sequence when Seal Team Six swoops into Abbottabad and raids the compound where Osama bin Laden had remained undetected for six years would definitely benefit from surround sound and a big screen.

And it would be fun to listen to the chortles of derision from a Pakistani audience in a real time, rather than following the tweets and Facebook updates of those who watched versions downloaded from the internet weeks before its release in the UK.

But I'm not holding my breath that Kathryn Bigelow's account of the hunt for America's greatest enemy will go on general release here any time soon. The film's distributors have not offered it for theatrical release in Pakistan over concerns that the official censors would take exception to it.

While the movie is controversial in the US over the suggestion that the CIA's "enhanced interrogation" techniques were instrumental in nabbing Bin Laden, in Pakistan the film is an unwelcome reminder of a past humiliation.

Pakistan's security establishment is still seething over the Americans's decision to mount a massive operation without bothering to involve the Pakistanis, nominally allies in the war against al-Qaida.

So, in Pakistan many people are making do with illegal downloads and pirated DVDs. In my local video shop it comes in two different cases. One has the original artwork on the cover; the other features a large portrait of Bin Laden, a character whose face is never actually shown in the film.

"For me the biggest problem was that the production design was so weak," says Wajahat Khan, a television journalist. Not only is he unconvinced by many of the locations used to stand in for Pakistan, Khan is, like many others, bemused by the depiction of Pakistanis speaking Arabic to each other. And he thinks the film-makers are guilty of "imagining Pakistan to be what they want it to be".

"It does a disservice to how complex the society is," Khan explains. "This society may have housed Bin Laden but it's not the backyard of a local mosque in Jeddah."

Expatriate life is also shown to be grimmer than the reality of large and spacious houses enjoyed by diplomats in Kabul. Perhaps the foreign press corps is to blame for disabusing Zero Dark Thirty's screenwriter, Mark Boal. During a visit to Pakistan before filming began, Boal asked a group of hacks whether foreigners in Islamabad enjoy "crazy parties where everyone gets naked in the pool". The poor man looked crestfallen when told the (all too depressing) truth that Islamabad is a pretty subdued place.

Although it was described by Bigelow as a "reported film", Zero Dark Thirty offers a feast for fact-checkers. Inaccuracies abound, largely due to the need to compress the decade-long hunt, create composite characters and make the whole thing work as a piece of drama.

A single character, Maya, is used to carry the film. She is portrayed as a lone voice challenging the CIA's bureaucratic inertia after Bin Laden trail goes cold and she is placed at the centre of the action. She is shown dining in a poor imitation of Islamabad's Marriott hotel even though it was blown up in 2008. Her car is attacked by gunmen as she drives out of her house – something that has happened more than once to US government employees in Peshawar, but not to anyone's knowledge in Islamabad.

One of the CIA's overseas "black sites" used for interrogating members of al-Qaida is shown in Pakistan itself, presumably to place Maya in both the torture scenes and where the action was in the CIA's Islamabad station.

Her character appears to be based on a real CIA agent named as Jen in an account of the Bin Laden raid written by former Navy Seal Matt Bissonnette. But Peter Bergen, a journalist and author who has researched Bin Laden more deeply than anyone else, claims the CIA officer who worked on the search for eight years up until his death and was convinced he was hiding in the Abbottabad compound was actually a man.

In December the acting director of CIA went public to criticise the film for taking "significant artistic licence, while portraying itself as being historically accurate".

The film, which claims to be based on "firsthand accounts of actual events" adds tantalising and colourful details that build on what has been reported elsewhere.

But it's hard to know what to believe when the film makes an astonishing error in portraying one of the gambits used to try and identify whether Bin Laden was hiding in Abbottabad. A controversial hepatitis B vaccination programme run on behalf of the CIA in the town in an attempt to get hold of Bin Laden family DNA is clearly shown as an anti-polio campaign. It's a truly sloppy mistake given how widely reported the incident was.

And it's also potentially dangerous. The scandal of the CIA using aid workers as cover for operations has helped to inflame deep mistrust in Pakistan's tribal areas towards vaccination programmes. Two Taliban commanders have banned polio eradication from their areas of control. In December, six polio vaccinators were murdered by gunmen while going about their work.

Another curious departure from the truth, likely only to be noticed in Pakistan, is the decision to rename the CIA's station chief in Islamabad who, as accurately depicted in the movie, has to leave the country after anti-drone campaigners blew his cover by naming him in a court action.

For some reason the film-makers name the character Joseph Bradley, not the real-life Jonathan Banks whose name is now irretrievably all over the internet. Could this be some small (but pointless) quid pro quo for the access Boal was granted to CIA officers and White House officials? Or just artistic licence?