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)
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)