The Enterprise is able to beam Spock aboard with its shields raised. Transporters do not work through shields.
The Enterprise and Discovery deploy far more shuttles than could possibly fit within them.
When she exits Discovery in the Red Angel suit, Burnham flies by the Enterprise close enough to touch its hull. The Enterprise's shields are still up. She should not have been able to get that close to it.
Captain Pike says "Calvary" for "cavalry," a singularly suitable mispronunciation on Good Friday.
The crew of Discovery realizes that the manner in which they powered up the time crystal means that it will burn out after a single use, and thus Burnham would be unable to return to their present from the future if she jumped there. Yet once she realizes that she needs to send out the signals that led Discovery to acquire all the elements it needed to complete the time-suit project, she is able to make multiple jumps, to each point in the past, and still have enough power to take Discovery into the future as originally planned.
The entire purpose of Discovery traveling to the future was to prevent Control from obtaining the Sphere date. Once Leland (possessed by Control) made it aboard Discovery, continuing the plan to travel to the future became counterproductive, as doing so would no longer prevent Control from obtaining the data. Once Leland/Control was destroyed by Georgiou, traveling to the future would be pointless, as there would no longer be any threat to safeguard the Sphere data from.
Spock recommends to the admiralty that all knowledge of Discovery and its spore drive be classified (an apparent attempt to reconcile the events of the first 2 seasons with established Star Trek canon). In season 1, information about the spore drive was disseminated to the entire fleet to try and aid the war effort against the Klingons. That would be millions of servicepeople with knowledge of the ship and spore drive, along with civilian contractors, families, etc. Even if they were all sworn to secrecy, it is mathematically impossible to maintain a conspiracy of that size.
Saru's sister and other warriors from Kaminar arrive to help in the battle, saying they received Saru's message. It was repeatedly stated that long-range subspace communications were down since well before Saru recorded his message.
The computer mispronounces the word "temporal."
Commander Chin-Riley states that if the torpedo embedded in the Enterprise's hull detonates, it would blow a hole "four decks wide" in the hull. Decks are stacked vertically, and while it may be possible to use that as a determination of depth, there is no standard deck measurement for width.
Dr. Pollar mispronounces Lt. Nilsson's name as "Nielson."