The Man in the Fallout Shelter - S1-E9
Plot hole: At first the victim (Careful Lionel) is described as not returning to pick up his new shirt in November 1958, and possessing love letters dated from 1957 through early winter (November) 1958. Booth reports the fallout shelter where Lionel's body was discovered was sealed in 1958. Later Lionel is described as reported missing by his boss in January 1960, and the illegitimate child he fathered was born in 1960 as well. That would mean his boss didn't notice he was gone for over a year, and his pregnant girlfriend was with child for at least 14 months.
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?
The Feet on the Beach - S6-E17
Plot hole: Dr. Filmore stated that he was reading on Thursday May 9th and his arm stopped working. May 9th hasn't been on a Thursday since 2002. Hard to believe that he would be working for almost 10 years with his arms being paralyzed.
The Woman at the Airport - S1-E10
Plot hole: The surgical instrument that killed 'Susan' was the same one used on her jaw during her plastic surgery. 'Leslie" would not have been able to get the instrument to use to murder her and then put it back in the case, since it was still in the office in the case when Bones and Booth came to get it.
The Recluse in the Recliner - S9-E24
Plot hole: In the beginning of the episode Booth is brought in by ambulances because he was shot. The episode flashes back and follows back through the events leading up to that. At the end of the episode he is arrested and accused of murdering 3 FBI agents who were coming "to serve warrants." In actuality Delta Operatives had tried to kill Booth. If Booth had been picked up at the scene of the battle by paramedics, the medics would have seen the dead bodies of the operatives in their gear and been able to easily prove Booth didn't just murder 3 agents. Furthermore, the medics on the scene would not just ignore the destroyed house and dead bodies. They would have called local PD and Booth would again be off the hook. (00:01:00 - 00:46:00)
The Secret in the Service - S11-E17
Plot hole: The chute is supposed to be so narrow that it injured the Secret Service agent's shoulder, but is wide enough for Hodgins to fit down comfortably in a sitting position.
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.
The Drama in the Queen - S9-E23
Plot hole: The bullet that killed the victim had plastic associated with the wound. This was explained by the fact that the bullet that killed the victim hit a lane divider as it entered the water, but at the end of the episode it was discovered that the bullet was fired from under the water, negating the possibility of it hitting a lane divider at the surface.
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.