The Brother in the Basement - S11-E2
Other mistake: Dr Brennan barges into the interrogation at the end of the episode. Aubrey exclaims out "Dr. Brennan" however, he exclaims before he has seen who it is. (00:33:10)
The Drama in the Queen - S9-E23
Factual error: The IP address shown is not possible. IP addresses are always XXX.XXX.XXX.XXX however we are shown an extra set of digits making it XXX.XXX.XXX.XXX.XXX.
The Prince in the Plastic - S7-E3
Other mistake: Brennan finds Angela assembling a child's toy. She asks "what is all this?" and Angela replies "this is a walking toy for my girl." But Angela didn't have a baby girl, she had a baby boy - Michael Staccato Vincent Hodgins. (00:15:00)
The End in the Beginning - S4-E26
Plot hole: We learn that Agent Booth has a brain tumor that has been causing him to hallucinate. One of the hallucinations mentioned was Parker in "The Hero in the Hold." At the end of the episode, Dr. Brennan both sees and speaks to Parker in the cemetery. Agent Booth believed Parker to be a ghost, and we were to believe that Dr. Brennan had unknowingly had a paranormal experience.
Suggested correction: The implication of that episode was that Parker's ghost was real, since Booth points out numerous things he does during his escape that he couldn't have done on his own. Dr. Brennan seeing Parker at the end of the episode confirms this. Dr. Brennan is the only one to posit that Booth's belief that he saw Parker was a hallucination brought on by his brain tumor, because she did not learn who Parker was when talking to him in the cemetery; Booth was looking the other way, all Brennan knew was that a young man walked up to her and said something about enjoying life. Even if she saw a picture of Parker at some later date, she probably wouldn't recognize him.
Two Bodies in the Lab - S1-E15
Continuity mistake: After Bones and Booth have a little argument at the crime scene, Bones takes her Dictaphone out and starts taking notes. When doing so she is holding the Dictaphone vertically. Camera changes and now it is horizontal. (00:06:00)
Two Bodies in the Lab - S1-E15
Continuity mistake: When Booth asks Bones what happened to seeing someone across the room, eyes meeting etc, Bones hand holds of the top of her clipboard. Camera cuts and her hand has vanished. (00:03:20)
Two Bodies in the Lab - S1-E15
Continuity mistake: At the start when Dr. Goodman interrupts Bones, her hands go from the keyboard to on the arm of her chair instantly. (00:00:45)
The Man on the Fairway - S1-E14
Continuity mistake: When Booth is talking to Max's son about how the simplest explanation is usually right, he is pointing with his finger, camera cuts and he is no longer pointing. (00:29:25)
The Man on the Fairway - S1-E14
Continuity mistake: When Angela walks over to the wood chipper she is drinking from her drink. Camera cuts and she has her arm with her drink in out to the side. (00:25:40)
The Woman in the Garden - S1-E13
Continuity mistake: When the man who put a hit out on Bones is ambushed by Booth, Booth's grip on his face changes instantly. Note the fingers in front/behind his ear. (00:39:30)
The Woman in the Garden - S1-E13
Continuity mistake: When looking for the plant Hodgins, Bones and Booth are in the 4x4 driving down the road. However in the shot of the car approaching the camera it is not Booth driving. (00:07:40)
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.