They really wrote themselves into a corner making Burnham a mutineer. This episode (and pretty much any episode after the third one) could have been told even if she were just a regular officer on the Discovery, and arguably would have worked better. It also seems like nobody gives a fukk that she's a mutineer except for Admiral Cornwell (and Saru for the first couple episodes), and the only other time it comes up is when she's introduced to a new character and they go, "Oh, you're THAT Michael Burnham?
" Tilly was looking to her for advice on how to be a Starfleet captain for Christ sakes. Burnham should be the last person to be asking that.
And now with Lorca offering her a spot on the bridge crew, that should be an interesting dynamic because nobody should be willing to fukk with her, but it'll probably get ignored for all the other storylines (finding the admiral, Klingon war, Lorca's self-destruction). I figured Lorca would either die or be relieved of duty by the end of the season (and he should because he's a piece of shyt), and it seems to be the direction they're going in, but if that happens Burnham goes right back to jail. There'd be no reason to keep her on the Discovery without Lorca vouching for her.
All that being said, I thought this was definitely one of the better episodes so far, which is good. I didn't like last week's episode at all.