Revealing mistake: When Copper is talking to Sam in the lobby, Cooper pulls out his phone to cancel his lunch date with Charlotte for that same day and his phone is time stamped as 7:35pm. (00:16:25)
Continuity mistake: When Violet is talking to the boy outside the school, he is holding a baseball bat. At one point he points the bat at her, but in the next shot the bat is on his shoulder.
Factual error: In the opening scene Addison and Pete are running on treadmills side by side. They are seen increasing their speeds to 8 mph and above. Addison even had hers to 10.1 mph yet they are both still talking, smiling, and laughing easily. 10 mph is a very fast speed for humans and they would not be able to laugh or even speak at those speeds. (00:02:10)
In Which Cooper Finds a Port In His Storm - S1-E8
Continuity mistake: While walking into the church Sam and Naomi discuss their sexual encounter "the day before." The day before when the encounter took place Sam had bruises and cuts on his face from being pistol whipped by the pregnant robber. There's no way he could have healed completely overnight. (00:08:50)
Revealing mistake: After Charlotte says the little boy has been dead for half an hour and Cooper calls the time of death, the boy moves his eyelids twice, and when his mother puts her arms around him he moves his arm a bit.