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)