
Character mistake: In the scene where Rick Marshall is playing the Banjo, he says he has been "doing some thinking with just him and the old four string". His banjo has five strings and you can see the five strings when he lays the banjo down.

Character mistake: When Tommy is being shown his new office the glass reads "Thomas R. Callahan III, " but when Tommy is introduced as the new President of the company he is introduced as "Tom Callahan, Jr." which would be his dad. (00:11:35 - 02:11:55)

Character mistake: In a scene when Watney is recording his video log, he imagines what would happen if his pressurized shelter suddenly would break. He concludes that he would implode, but the correct wording would be explode.

Character mistake: After Fleming has murdered his wife, he warns his girlfriend not to touch anything in the apartment, but he hands her a drink which he already prepared for her. At his direction she also makes a telephone call, holding the receiver with a cloth he hands her, but dialling the number with her bare fingers. On top of that, he hands her a pair of gloves after she has made the call - she would have touched or handled all sorts of things in the room by then. Why didn't he hand her the gloves as soon as she stepped in the room?
Suggested correction: This is a subtle hint that Fleming is preparing to frame his girlfriend for the murder. He would admit to having an affair with her (not a crime) but is going to deny any involvement in his wife's murder. (SPOLER ALERT!) Later he makes it clear that his girlfriend meant nothing to him and he didn't care that she had committed suicide (or so he thought).
Nowhere in the episode is this sub-plot explored or even mentioned.
Not only that, but the idea he was going to subtly frame his girlfriend doesn't make sense because he used her to establish his alibi. He tried to make it look like she was killed by an random intruder.

Character mistake: When Maximus is talking to Marcus Aerelius, he mentions that his wife has black hair. But in the scenes where we see her, she actually has brown hair. (00:24:40)

Character mistake: When Stan inflates himself, Michael asks, "How'd he do that?", implying that he doesn't know the rules of the Looney Tunes world. Since Michael was rolled into a ball by the aliens earlier in the film, this shouldn't be too much of a surprise.
Suggested correction: When Michael was rolled into a ball, he wasn't concerned with how that was possible and soon after he forgot about it. He was more concerned with dealing with the Monstars at the time and, in particular, helping his cartoon friends preparing for the game. When Michael witnessed Stan being flattened and inflated, it looked particularly strange and unfamiliar to him, unlike before as he couldn't watch himself experiencing being rolled into a ball. And that is what triggered his response about questioning how it was possible.

Character mistake: The police claim the Myers house is at "45 Lampkin Lane." The address on the front porch clearly displays the number 709.

Character mistake: Those are the most haphazardly secured cases of nitro I've ever seen in a movie. Couldn't they spare a shoelace or duct tape to secure the top?

Character mistake: In one scene, Ashley looks into Mr. Turner's yard with binoculars. She looks through the large glass circles. That would result in seeing everything smaller. If you want to see everything bigger, you are supposed to look through the small glass circles.

Character mistake: When Jimmy explains to the kids of the town where the aliens took their parents, he mentions the origin of the aliens being somewhere in the Orion Star System, 3 million light years away. The Orion system is way closer than that. It is actually less than 1400 light years away from Earth. 3 million light years away would place them further than the Andromeda Galaxy.
Suggested correction: This shouldn't be a character mistake. A genius like Jimmy would know something like this. It's basic astronomy.
That's exactly why it's a character mistake. A character mistake is when a character does or says something that they shouldn't based on who/what they are suppose to be, or something a character wrongly states as fact when they should know better.

Character mistake: There is no way an operative of Q's position and experience would have plugged a device taken from a bad guy into their network. Especially as they had had a security hack only a few days earlier, and this was a security establishment. It would have been thoroughly tested and checked on a stand-alone, air-gapped setup first.

Character mistake: Mother Nature tells Snow Miser to let it snow in Southland, it should be Southtown. (00:39:56)

Character mistake: All the characters wearing gas masks are wearing them with the straps over the hoods. I was army trained, and you always wear the mask next to the skin for best seal, with the hood over the top.

Character mistake: Some characters use the letter "s" at the end of a Pokémon's name when the plural of a Pokémon is just its name. The best example is when Pikachu says, "Roger must've sent the Greninjas to cause the car crash." Being a Pokémon himself, there's no way Pikachu, out of all characters, would say that.

Character mistake: Jeff mentions Mathias could have septicemia which he says is "a bacterial infection usually in the bone" However as a medical student he should know that septicemia means blood infection and has nothing to do with the bone.

Character mistake: When the Grand High Witch and her assistant enter her room while Luke gets the formula, they're wearing pointy shoes. Earlier, it was mentioned that witches never wear pointy shoes.

Character mistake: Jonesy says he read about Amber going to West Point. She was a Marine, and not in the Army, which is what West Point is for.

Character mistake: When Mike's wife is watching the news about the oil rig on fire, you can see the TV with part of the U.S. map on it and 'Mississippi' is misspelled as Missisippi. (01:09:10)

Character mistake: Dylan is showing Agent Cowan and the FBI director the pictures of the pigeons and Dylan and Cowan start arguing, while the FBI director continues to look at the evidence on the Four Horsemen. Whilst looking there is an article reading "FBI Investigation Stalls." On the first column of the article, it is mentioned that all four members of the Four Horsemen, J. Daniel Atlas, Henley Reeves, Merritt McKinney and Jack Wilder, all disappeared into thin air at the final magic show, and gave the audience fake dollar bills. By the time of the final magic show, Jack had faked his death and was presumed dead, so only three members of the Horsemen were present, not four. (00:08:55)

Character mistake: When Bruce is looking at Chase's various clippings of Batman on her desk while she's tending to the tea kettle, there is a paper that says "Diagnosis Form #39," and just above it, the word "schizophrenic" is incorrectly spelled as either "schizofrenic" or "schizoprenic" (a metal clip is partially covering the last six letters of the word, so it's hard to determine whether it's an "f" or a lone "p" where the "ph" should be). (01:03:11 - 01:03:32)
Suggested correction: It is possible (probably not common) to be a "III" and a "Jr." If you are named after your father, and he is still alive you are a Junior. If you both share the name with another member up the family tree say your great grandfather, then your father would be a "II" and you would be a "III." But since your father is still alive, you can still go by junior. I've known one person in this situation.
I guess you missed the part of the movie where his father died. He's made the new president because his dad is dead, not alive, negating your main point.
Bishop73
His dad literally just died, and most people don't know the specifics of the naming rules. That would be a character mistake of the person introducing him.
When Tommy is made president and introduced, that's at the end of the film. So, no, his dad didn't literally just die. Plenty of time passed. But the correction is wrong on its premise, but that's not to say a different argument couldn't be made why the mistake is wrong.
Bishop73