Character mistake: Although great care was taken to duplicate Bob Crane's distinctive hairstyle for Greg Kinnear, Bob Crane's hair was actually parted on the left. The makeup department for this film parted Greg Kinnear's hair on the right, producing a mirror-image of Bob Crane's hairstyle.
Character mistake: During the funeral at the end before the 21 gun salute, the NCOIC called for "half left face", that would cause everyone to get shot in the face.
Suggested correction: Half-left face means a 45° left turn (left face is a 90° turn), so wouldn't result in anyone getting shot.
Character mistake: When we see the relative positions Eddie and Johnny have, Eddie appears to be the one that should have done the signaling to the patrol car instead. (00:55:40)
Character mistake: When Ethan Thomas objects to Dr. Adanie's testimony, he does so on the grounds of "silliness." Silliness does not fall under the federal rules of evidence, and any lawyer worth their salt would know this.
Suggested correction: During the Manson trial in real life, the prosecutor objected to a completely pointless question the defense asked a witness on the grounds of being ridiculous. The judge agreed and sustained the question. In his book Helter Skelter, Bugliosi even acknowledges there's no such rule, but the judge sided with him. The prosecutor in this film is grasping at straws, since nothing that would fall under the rules of evidence would apply to his objecting to her scientific testimony.
Not true, he can object on the grounds of relevance. The YouTube channel Legal Eagle, which is run by an actual lawyer, even stated so. The same logic applies to the Manson trial. If a lawyer feels that a question is ridiculous, they can object on the grounds of relevance.
In a case involving demonic possession as a central aspect of the defense, there's no way relevance could be grounds to object to her testimony. Her testimony dealt with possession from a scientific point of view, but he objected because it was for the defense. The judge in the film even allowed her testimony stating that they'd heard a lot of scientific evidence supporting the prosecution's case and it was fair to hear from an 'exorcism expert'.
As for the Manson case, try reading the book written by the prosecutor. It even states in the transcripts that he objected on the grounds of a question being ridiculous (even if, in the end, it would actually be relevance).
Just because a lawyer in real life was able to successfully object on the grounds of ridiculousness doesn't mean it would suddenly become a good practice. That would be like saying basketball players should just wantonly heave half court shots, because sometimes they go in. The premise of your suggested correction was also that the lawyer had no legal grounds to object on, and that is objectively false. As I mentioned, the lawyer behind the LegalEagle YouTube channel even said otherwise.
Character mistake: When The Plague starts talking at the meeting and comes up with the story about a hacker planting the virus, he first says that an "unknown intruder" was the one who broke in, but only minutes later says that the cops picked up him already. (00:34:40)
Character mistake: When travelling between zones, they go 12 - 10 - 9 - 8 - 7 - 5 - 4. Which is the only route you can take that includes zone 8 as shown. This is silly as there are quicker routes such as 12 - 7 - 5 - 4.
Character mistake: At the beginning of the movie you can read the rules of the premises, in particular rule number 3 says; "No guns or any type of weapon permitted through the gates." However, the Wolf King's cronies dump their guns before the gate even when they were never supposed to be able to come in (so does Burke at the beginning, but he was trying to be admitted in). (00:07:15)
Character mistake: Dr. Bessner tells Linnet that the Eastern statue she'll see at Abu Simbel is 'the vocal statue', which emits a sound at sunset. The statues the doctor mentions are the Colossi of Memnon, over 500 kms north of Abu Simbel, so the movie here mixes up two very different monuments. (00:49:30)
Character mistake: When Henry Fonda is led to his cell, shot in a prison in Queens, a real inmate yells "What'd they get ya for, Henry?"
Character mistake: When Darcy walks into the police station the chief calls her Joan, the lead actress' real name, by mistake.
Character mistake: The banner of the fundraiser event for the Gotham upper class says "Childrens Hospital", no apostrophe. (00:11:55)
Character mistake: When Spade leaves Brigid in her hotel room, he says he will buzz her buzzer long-short-long-short, so she will know it's him. When he does return, he only buzzes long-short.
Character mistake: When Harry walks up to look in the car which Ricca and his men were shot in, he places his hands on the driver's side and back seat passenger's side window sill, while the crime scene is being investigated. No senior Inspector like Harry would do this. (00:09:40)
Character mistake: After the scene at the obese accountant's place, Rita is going through the case with Mike. She says, "Judge, prosecutor, criminal informant, the captain and you." She didn't mention the forensics expert, who is also on the board. (01:04:35)
Character mistake: The man on the phone told Mr. Lee he wanted $960,000 cash plus $1,726,000 transferred into his account. Because the Deputy Manager was killed when the bomb in his car exploded, Mr. Lee was later told he had to pay for his share, another $1,726,000 - so he needed to transfer $3,456,000. But $1,726,000 + 1,726,000 = $3,452,000. (00:11:20 - 00:20:32)
Character mistake: When Jesperson imagines himself as a Mountie his uniform is completely wrong and is not even the right colour. As it was his ambition to join the force and he has photos of RCMP officers in his cab, it seems unlikely that he would imagine himself in a completely incorrect uniform.
Suggested correction: It's not a character mistake, for the reasons stated; it's a clear factual error from the filmmakers.
It's a character mistake since it's his imagination and, as you stated, it's not something the character would get wrong.
Character mistake: Luca calls Eve in the dark outside the house, searching her. But they all know that Eve is deaf. (00:33:20)
Character mistake: In the first fight, there's a reaction shot where Speed shouts jubilant "Yes, yes!" when his own fighter misses with his attack and doubles over hit by a painful kick in the gut. That's a mighty weird thing to cheer on. (00:07:00)
Character mistake: Cross knows (for some reason) by memory the last words of the Lindbergh kid kidnapper (and killer) and that Soneji/Mercusio referenced in a book he finds in amazingly oblique ways. He calls him "Richard Bruno Hauptmann", while his name was actually Bruno Richard Hauptmann. (00:42:30)
Character mistake: The end credits (which are also IMDb's source) have the protagonist as "Detective Lucas Boyd." However, in the movie, his name (see the nametag on his desk) is spelled "Lukas" with a K. (01:01:05)