Also, there are two main points where the "acting" issues can probably be put down to the editing: when Georgiou is saying on the planet that they should consider Burnham getting her own command, the words "Commander Burnham" are totally editing in from somewhere else. Also the exchange of "Starfleet doesn't fire first" ..." we have to" is probably chopped together. There is no way to get a sense of the acting quality from this trailer as it is so chopped up. But that is a teaser trailer for you.
So true! Happens all the time in trailer edits