The Man in the Fallout Shelter - S1-E9
Character mistake: Hodgins is talking to Bones and says something about Goodman not being able to see his family and Zach not being able to see his kids. Goodman has kids, Zach was going to visit his family, not the other way around.
Suggested correction: With Zack's kids, Hodgins was referring to the 40 cousins and nephews that Zack has, and sees every Christmas.
The Boy with the Answer - S5-E21
Continuity mistake: It is the evidentiary hearing, all characters are put on the witness stand so you get to see what all of them are wearing. The trial starts the next day and lasts at least three days, but when they are in court at the end of the trial for the reading of the verdict for the gravedigger they all have the exact same outfits on as the day of the evidentiary hearing.
Plot hole: Angela comes into the autopsy room to inform Hodgins and Cam that Brennan is awake. Cam says that Brennan said the entry wound was cold and Hodgins comes up with the ice bullet theory. But how did Cam know what Brennan said about the cold if she didn't already know Brennan was awake?
Suggested correction: Bones told Booth that the entry wound was cold when she woke up. It's only fair to assume that Booth called Cam and told her.
But then, Cam would know Brennan was awake making the whole point of Angela coming in to tell them pointless. Plus with Cam knowing Brennan is awake, why would she not tell Hodgins?
I'm rewatching and have been looking for an answer as well. I think it's just a continuity error. If Booth told Cam, she would've told Hodgins, and when Angela walks in to ask if they made any progress, Cam would also tell her. Having Angela tell both Cam and Hodgins that Booth told her, then seeing them relieved and having Cam mention Brennan saying the shot was cold makes no sense other than they wanted to keep it as a dialogue instead of a monologue. Which makes it a pure error.
Revealing mistake: The producers have not taken enough generic shots of the places the gang hangs out at; the Royal Diner, & the Founding Fathers. If paying attention (or, watching multiple episodes in a row), one will notice the same people wandering down the street an awful lot! As well, outside the Royal Diner, there's a weird-shaped street corner, that appears to force all traffic in front of the Diner. This would be due to the size of backlot being limited, and certainly doesn't look right.
The Next in the Last - S10-E22
Character mistake: Booth states that Pelant used to communicate via flowers. However it was Bones and Angela that did, not Pelant. (00:04:00)
Suggested correction: Actually, When Pelant is leaving for Egypt, he gives Brennan a flower to communicate grief and loss, so Pelant did in fact communicate with flowers.
Actually, this is what is accurately said 'Exactly what Pelant used to use to send a message' in reference to the flowers, if it were 'what Pelant used to send "messages" then yes, your point would be more accurate. Yet the wording suggests that it was 'a' message he sent, not plural, single. Which he did.
Audio problem: When Bones wears the dead guy's hand, Bones says a line about not needing mittens for Christmas. However the audio doesn't match her mouth. (00:07:20)
The Pain in the Heart - S3-E15
Character mistake: Zach, from his hospital bed, says he used 3 grams of the monomer to make the explosion. 3 grams of a powder would be a very small amount; less than a teaspoonful. But when he actually did use it, he took a loose amount in a large tablespoon. Zach would have carefully measured it in order to be precise; but he did not. So this is a factual error in what he says; it is also a character mistake in that Zach is the personification of technical accuracy, and would never take a casual spoonful - especially of an explosive.
Suggested correction: Given subsequent revelations, this could be said to be part of everything that goes on.
The Doom in the Boom - S11-E10
Plot hole: Dr. Vizeri leaves the Jeffersonian months prior to this episode (confirmed in the episode) however, after turning up unannounced he still has his work jacket. It is unlikely his jacket would still be there. (00:20:05)
Suggested correction: It is not unreasonable to assume it was simply put into storage rather than being thrown away. It was perfectly usable and could have been used by another member of staff if theirs was unavailable.
I've forgotten the exact circumstances of Dr. Vizeri's departure, but the Jeffersonian probably would not have a policy that required personalized work clothing to be returned. Dr. Vizeri indicates in the episode that it had been his strong desire to return ever since his departure, so it is likely that he would have retained the garment for practical, or at least sentimental reasons.
The Skull in the Desert - S1-E17
Revealing mistake: When they find the body of Joesph, you can see him breathing despite him being dead. (00:15:50)
Suggested correction: Joseph is not dead, he's just beat up.