Under & Out - S3-E11
Plot hole: Gretchen, Lincoln, and Sophia were able to visit Scofield and Whistler in Sona without Gretchen being recognized. She was taken in for questioning in episode 9, but she managed to escape and kill General Zavala and one other guard. The other guards knew that she was the one who killed Zavala but she was still able to sign in for visitation.
Be Afraid of the Dark (2) - S3-E12
Plot hole: When the Corrodium Beam is shut down, there is a brief scene of the sky clearing at Mount Rushmore. But on the cliff face all four heads are seen, whereas the head of Theodore Roosevelt got crumbled in "Secrets," and it's too far forward to have been carved into the mountain face, in place (and same position) of the old head, yet again.
Plot hole: The ages of the children on the show are really inconsistent. When the show starts in 50 BC, Octavian is around 12, Lucius is an infant and Vorena the Younger is at least 8 (given that she must have been concieved before Vorenus left for Gaul). Three years later Caesarion was born. When Simon Woods takes over the role of Octavian, Octavian is around 19, as stated on the show. Lucius should be seven but looks like he's four and Vorena should be fifteen but still looks eight. Episode 9 of season two takes place in 32 BC, 18 years after the first episode. Octavian might very well be 30, but Lucius (who would be 18) is around seven, Vorena (who would be 26) is a pre-teen and Caesarion (who would be 15) is around eight. Even if the events were moved up so that episode 9 is actually set earlier, the ages of the children still don't match when compared to how much the other characters have aged.
Recognition - S1-E17
Plot hole: Bridge could have used his powers to figure out if Wootox and Sky's bodies were still switched.