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 Predator in the Pool - S5-E18
Character mistake: When Bones and Dr Hodgins, who is proclaimed as a seasoned diver in a previous episode, are in the tank, Bones gives an instruction and Hodgins replies with a thumbs up. Since Bones is diving as well, they both would know from certification (without which neither would be allowed to dive in the facility) classes that a thumbs up is the hand signal for "I'm ascending", not OK or any form of acknowledgement. They either are not certified divers or they should have immediately surfaced. (00:06:30)
The Man in the Fallout Shelter - S1-E9
Continuity mistake: Bones puts the skull down on the table facing to the left. Camera cuts and the skull is facing to the right. (00:00:45)
Continuity mistake: Angela asks Bones what the rush is. When she does, Bones' ponytail is down her back. Camera changes angle and now it's over her shoulder without moving her head. (00:12:45)
Continuity mistake: When Booth is interviewing The Man in the Wall, he is stood to the side of the door. Camera changes and now he is in the middle of the door. (00:33:50)
Continuity mistake: We see Bones draw a chalk outline on the floor and it is fairly faint. When we next see it, the lines are a lot more refined. (00:30:30)
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)
Revealing mistake: When Hodgins is explaining about decomp gasses, you can see in one shot Angela is mouthing his lines. (00:18:10)
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.