According to the captions, Leland refers to L'tak Terai as a "spatial and order dysphagia, similar to dyslexia". Dysphagia is a disorder of swallowing, while dysphasia is a disorder of speech. Dysphasia is the correct term.
Spock's hair and beard are overgrown to show his deteriorating mental state and the length of his isolation, yet the neckline of his beard has been recently shaved clean.
Amanda tells Michael that she won't take Spock to a hospital because they would turn him in for trial. Later in that same conversation she says that under Federation law, she can claim diplomatic immunity to shield Spock from being extradited. If that is the case, she could still take him to a Vulcan hospital without him being extradited for trial.
In her opening monologue, Burnham states that they now know that the Red Angel is from the future because Saru saw it and identified it as a humanoid wearing an exo-suit more advanced than anything in the Federation. Just because it is more advanced than current Federation technology does not mean it comes from the future. It could have just as reasonably come from a contemporaneous civilization that is simply more technologically advanced than the Federation, just as the Federation is more advanced than the Ba'ul and the Vulcans were more advanced than humans when they met.
Burnham wonders if Spock is saying numbers in reverse, and supposedly tests this by typing a number into a Starfleet computer and finding a match. But there are 100 billion stars in the galaxy, so any number would match - like dialing a phone number, and being proved correct because somebody answers the call.
Pike reasons he is the most qualified person onboard Discovery to pilot a shuttle towards the temporal anomaly because his first assignment in Starfleet was as a test pilot. At this point in his career, he was decades removed from that assignment. There are plenty of people aboard with more recent piloting experience who would be more qualified to fly the mission without risking the ship's captain.
Leland calls Spock Commander when he is still a Lieutenant.