Continuity mistake: At the very start Bones is holding the microphone and its pointing towards her. Next shot, Dr Goodman has the microphone pointing at him. (00:00:40)
The Murder of the Meninist - S11-E12
Other mistake: Cam is burning a pork human analogue which is alight with flames. When the analogue explodes and covers Hodgins in meat, he is not burnt by the searing meat. (00:27:25)
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 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.