Earthshock - S19-E6
Plot hole: The Cyber Leader states that he needs the Doctor to pilot the TARDIS. It makes no sense then, that he would try to kill the Doctor once inside, and before the TARDIS had landed in a safe place. (01:33:55)
Plot hole: During the 3/29/05 episode, the MetroCourt restaurant is cordoned off as a crime scene following the mob hit. Regardless of the fact that the restaurant is sealed off with crime scene tape and police are present gathering evidence, three characters (Alexis, Diego, and Maria) manage to walk past the crime scene tape and past the cops into the restaurant. Alexis is there taking pictures of the crime scene, even though she is not an employee of the police department nor the DA's office. Maria is there going about her business as manager of the restaurant and Diego is hanging out having a conversation with her. At no time does a police officer ask any of the characters to leave the crime scene area.
The Man Who Was Never Born - S1-E6
Plot hole: Andro has memorized "every detail" of Cabot Jr.'s life, including his mother's name, Noel. Yet when he travels to the past, meets Noel and learns her name, he still mistakes Cabot Sr. for Cabot Jr., who isn't born yet. Having memorized all those details, he would have known the moment he met her that Noel was Jr.'s mother. Andro's confusion makes no sense. (00:28:00)
Second Sight - S4-E7
Plot hole: Kimble enters the bar in the midst of a fight between photographer Howie and a man he tried to blackmail. Kimble comes in too late to hear what the scuffle is about, yet after breaking it up, he somehow knows all about the incriminating photo that sparked it. (00:06:00)