The length of Rick Flag's hair constantly changes from short to medium, revealing that those specific scenes were re-shoots.
(at around 4 mins) Waller has dinner with an Admiral with a name tag on his uniform naming him "MacKensie" but the credits name him "Olsen."
(at around 48 mins) When the helicopter heading into the city, the camera shows Harley holding a phone with a message from Joker. A close-up of her hand shows her thumb and thumb nail bare. A few scenes later when they begin to shoot the cannon fodder, Harley's nails are painted.
June Moone's last name is spelled "Moon" in the credits.
(at around 45 mins) In the airport Harley Quinn has long, bleach-blonde hair. After putting on her t-shirt, it is now much shorter and has multi-colored highlights.
(at around 21 mins) Enchantress steals a top secret document from the Iranian government, but its pages are bound on the left side, which is the wrong side for texts written in Farsi.
(at around 1h 45 mins) Military-grade explosives do not explode when shot at; they require a blasting cap to be set off. This is a safety feature of such materials. Deadshot would know this with his expertise.
Harley is a psychiatrist, which means she completed both medical school (8 years of undergraduate and medical studies) and a residency in psychiatry (another 4 years). Not only that, she was competent and experienced enough to be allowed to treat high-risk criminals like the Joker, hinting at a reputation that she must have worked to build for some time. Plus she's been a part of the Joker's gang for at least ten years, since she was mentioned as an accomplice in Robin's death, which took place that long ago - and yet she's twenty-six. This is possibly justified. Joker doesn't appear to have aged much either since they met, and Harley regularly displays abilities that few normal humans, let alone ones with no training, which may imply that the acid they fell into changed their physiology.
Similarly, Enchantress' human host has a Ph D (given she's referred to as Dr. June Moone), another process that takes several years to achieve, and only after completing at least one postgraduate degree. It is fairly possible to have achieved a doctorate by your late twenties, depending on your field, but an archaeology Ph D in the United States typically takes about a decade to complete. And June's played by Cara Delevingne, who in real life was twenty-three at the time of filming and only a year or two older than most new college graduates (depending on how long an undergraduate degree takes to complete).
(at around 5 mins) Waller refers to Deadshot as being "most wanted". But he's in prison, so he's not wanted any more.
(at around 26 mins) When Deadshot is practicing with weapons while still being incarcerated, no one is wearing hearing protection. This is required in any facility where firearms are shot, and it surely should have been enforced in a government-run prison facility of all places.
(at around 21 mins) When Enchantress brings the binder from the Weapons Ministry Vault in Tehran to the Chairman, he opens the book left to right. The book would be all in Persian, meaning the folder would open right to left, following Persian script. But the Chairman wouldn't necessarily know that, so he'd open it the way he's used to opening books.
(at around 19 mins) The overview of the Pentagon is shown with the text on the left bottom corner "THE PENTAGON WASHINGTON DC" - though the Pentagon is in the county of Arlington, Virginia.
It has been insisted by many, that the building is not only physically close (to Washington D.C.), but is so linked to the city's economic and political culture, that the employees think of themselves more as 'Washingtonian' than 'Virginian'. Additionally, in reality, at least two seals of the building (one's in the press room) state "Washington" (or "Washington DC") at their bottom, making the identification not entirely wrong.
It has been insisted by many, that the building is not only physically close (to Washington D.C.), but is so linked to the city's economic and political culture, that the employees think of themselves more as 'Washingtonian' than 'Virginian'. Additionally, in reality, at least two seals of the building (one's in the press room) state "Washington" (or "Washington DC") at their bottom, making the identification not entirely wrong.
(at around 2 mins) Griggs refers to his men as guards rather than COs (corrections officers) or officers. On the sign for Belle Reve it says Special Security Barracks, a military installation. As a military installation all personnel are corrections specialists and would be referred to by their individual ranks, collectively they would be referred to as guards.
Joker's skin and hair are the color they are as a result of being exposed to chemicals, hence why he still looks that way in Arkham. But when his hands are shown, they are flesh-colored instead of white.
(at around 1h 15 mins) When Harley Quinn falls from the chopper, lands on the roof, rolls and then begins running again, it is clearly a male stunt double.
(at around 13 mins) Harley Quinn is thrown half through the windshield of the Jokermobile. The glass is broken like plate glass, while a real windshield is made of laminated glass, and does not fracture into large shards as shown.
(at around 1h 35 mins) When Incubus throws Deadshot into the chunks of concrete, they bounce slightly when he lands on them, indicating they are foam props.
(at around 1 min) Harley still keeps her legs and armpits clean shaven while imprisoned in an empty cell with no amenities.
(at around 41 mins) Just before Incubus knocks a HMMWV onto him, a US soldier is seen firing at Incubus with his M4 carbine, but there is no sound for the undoubtedly loud gunfire.
(at around 9 mins) In Harley Quinn's file (her introduction sequence), her date of birth is listed as July 20, 1990. This would put her around 26 in 2016. The following scene has her arrest date as 10/13/14, putting her around 24. It is mentioned she is a psychiatrist prior to meeting the Joker. It takes approximately 8 years of medical study in the United States to become a psychiatrist. Unless she has an extremely high intelligence and started medical studies at only 16, this is an unrealistic time line.
Apparently none of the inmates are allowed to leave their cell, yet none have a toilet.
(at around 15 mins) When introducing the squad, Killer Croc's activity report states he was over seven feet tall at his latest incarceration, although throughout the movie he is near the same height as everyone else, as Adewale Akinnuoye-Agbaje height is actually 6'2.
(at around 3 mins) When a car arrives at a building, Waller's bodyguards are egregiously deficient. As she exits her vehicle a guard armed with an automatic rifle allows her to cross in front of him, blocking his view and putting his primary in a potential crossfire. Moments later she approaches a door flanked by two similarly armed guards, both of whom turn their back on the threat zone to open the door for Waller--who is perfectly capable of opening a door for herself. These are both major breaches of bodyguard protocol.
(at around 11 mins) Jared Leto's real tattoos are visible in multiple scenes. Most notably, the triad logos on both of his forearms are seen through the shirt during the strip club scene.
(at around 14 mins) In Captain Boomerang's Activity Report being presented by Amanda Waller at the beginning of the movie, the first line of the second paragraphs calls him "Hawkness" instead of "Harkness". Elsewhere in the report, the name "Harkness" appears correctly.
(at around 51 mins) When Harley says "that's a killer app", Flag reminds them that they have explosives implanted in their necks. Harley then touches the left side of her neck, while the device was implanted on the right side.