Plot hole: If the Lady of the Lake walks every night to her room and kills those in her path, why didn't Flora and Miles' parents die in their room by the hands of the Lady in the Lake when they first moved in?
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.
Plot hole: The police are looking for school shooters who wore unicorn masks. There are cell phone recordings of the individuals shooting and I believe CCTV recordings from inside the school. There is a forensic science technique of accurately estimating suspect(s) height(s) using CCTV/camera recordings and math to determine the height. The police could have further narrowed down their pool of suspects by using this forensic method, but they are going at the students blindly chasing dumb leads.