Continuity mistake: After accidentally setting of the Abomination alarm, Amity and Emira run over to see what's happening. However, Amity has her normal hair, when she is supposed have a bun. This is fixed in the next scene. (00:13:18)
Plot hole: Dr. Adam Soong is initially presented as a discredited scientist, banned from the scientific community; he gets debarred and his funding revoked. And it's not an internal matter; he is publicly exposed for it. His daughter in episode 6 even finds out this information on Google. Several news articles call him "mad scientist" and such. However, this same person at the same time throughout the rest of the season has every bit of pull and influence, not just through undercover channels, but is treated with the utmost honor and deference by the NASA PR people at public events.