Harbingers in a Fountain - S5-E1
Continuity mistake: Brennan has just returned from Guatemala and is back at her office. She meets Booth and the two hug. The way they hug each other differs between shots, most notably the position of Brennan's right elbow on Booth's shoulder. (00:04:00)
Two Bodies in the Lab - S1-E15
Continuity mistake: At the lab, after the body has been brought in, Bones is looking at the feet in the cement. Her ponytail is messily tied. When she tells Zack that she'll be busy that night, her hair is now neatly tied. (00:02:05)
The Priest in the Churchyard - S2-E17
Continuity mistake: At the diner, after Dr. Gordon has told Bones and Booth the problem with their relationship, the two shares a triumphant hand slap. Bones' glass refills itself between shots.
The Girl in Suite 2103 - S2-E6
Continuity mistake: When Booth and Brennen are questioning the Senator's son, the cap on the bottle of water keeps switching from being on and being off between shots.
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 Graft in the Girl - S1-E20
Continuity mistake: The assistant transplant coordinator tells Bones that another woman, Kelly DeMarco, had the same bone graft donor as Amy's. In the scene where they are analyzing the bone from Ms. DeMarco, Zach says she 'died of lung cancer 2 months ago.' Less than 10 seconds later, Booth says that she 'never smoked a cigarette in her whole life, only to die of lung cancer 8 months ago.' (00:14:50)
The Critic in the Cabernet - S4-E25
Continuity mistake: Hodgins and Fisher are discussing how hard it is to remove wine stain. Hodgins' rubber gloves are very dirty. When Fisher realizes how to clean the bones, Hodgins' gloves are much cleaner, only stained around the finger tips.
Two Bodies in the Lab - S1-E15
Continuity mistake: Booth, Hodgins, and the police are gathered outside the abandoned building and are discussing tactics. Booth has a medal around his neck. It pops in and out of his jacket between shots. (00:37:00)
Stargazer in a Puddle - S2-E21
Continuity mistake: In the establishing shot of the church where Angela and Hodgins are having their wedding, the walls are all white. When they flee the wedding, the exteriors are red brick. (00:36:00)
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.
Factual error: When Angela is running her computer model of the victims' chase behind the wall in the club, she says it "got tight in there - 15 centimetres." 15cm is 6 inches. It isn't possible that a grown adult could pass through a path that narrow - it would have to be at least twice that, just to breathe in & out. (00:24:50)
The Dentist in the Ditch - S5-E13
Factual error: Booth is introduced to Padme, Jared's girlfriend from India. She explains that they met when they were in "Bangalore visiting the Karnataka Belur temple". Bangalore is the capital city of the state Karnataka. Belur, however, is one of the twin temple towns of Belur and Halebid which is in the district of Hassan, a three-hour drive from Bangalore. There is no Belur temple in Bangalore. (00:06:00)
The Knight on the Grid - S3-E8
Continuity mistake: Amy comes to see Brennan at night to tell her about her daughter's sickness. There are a bunch of letters on the kitchen counter. The envelopes move around in between shots, most noticeably the brown one. (00:03:20)
Factual error: Dr. Wexler is killed in his flat in Oxford, yet the the fire engine outside his property is marked as being from the London Fire Brigade rather than the Oxfordshire Fire and Rescue Service. (00:04:20)
Player Under Pressure - S3-E11
Audio problem: As he is preparing to put the skull in the turkey carcass, we hear Hodgins telling Cam that he is wrapping a skull in a turkey carcass, but his lips don't match the words "turkey carcass." He is saying something else.