After the minefield incident, Lt. Joann Owosekun reports that there are five injuries and no casualties. The definition of casualty is a person killed OR injured. Therefor she should have said: Five casualties, no fatalities.
If Control was in command of all of the Section 31 headquarters' functions, it would also have transporter control, and could have beamed Airiam back onto the station before she died.
Admiral Cornwell states that Admiral Patar is a member of the "Logic Extremists." The Logic Extremists are a known terrorist organization on Vulcan. A known terrorist would not be allowed to hold any military position, much less one with such a high level of authority. It makes no sense for her to even be a member of Starfleet, as the Logic Extremists' main operating theory is that humans and other outside influences are detrimental to Vulcan and Vulcans. They push for Vulcan to withdraw from the Federation and isolate itself from the galactic community. Starfleet is the defense and exploratory service of the Federation and is comprised largely of humans and other alien species.
Tilly reports to the captain that Airiam has downloaded her personal memories to the main computer, but the correct term is that they were uploaded.