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.
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 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.
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?
Suggested correction: Bones told Booth that the entry wound was cold when she woke up. It's only fair to assume that Booth called Cam and told her.
But then, Cam would know Brennan was awake making the whole point of Angela coming in to tell them pointless. Plus with Cam knowing Brennan is awake, why would she not tell Hodgins?
I'm rewatching and have been looking for an answer as well. I think it's just a continuity error. If Booth told Cam, she would've told Hodgins, and when Angela walks in to ask if they made any progress, Cam would also tell her. Having Angela tell both Cam and Hodgins that Booth told her, then seeing them relieved and having Cam mention Brennan saying the shot was cold makes no sense other than they wanted to keep it as a dialogue instead of a monologue. Which makes it a pure error.
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 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 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 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.