Plot hole: They only take out the shrapnel from the gut shot - they never deal with the shrapnel in his shoulder at all. (00:04:25 - 00:05:00)
Left Behind - S1-E9
Plot hole: It's revealed that Chronos is Mick from the future after he was abandoned by Snart. However, in the episode White Knights (episode 4) the earlier version was able to sneak up on Chronos and surprise him with an attack from behind. If that was a future version of Mick then surely he would have remembered the attack coming and could not have been so easily caught off guard.
Lidar + Rogues + Duty - S3-E16
Plot hole: Riley's father Ellwood shows up unannounced at Phoenix headquarters. The address for the Phoenix Foundation Headquarters is classified, as is Riley's job. How did he know where to go? (00:22:10)