"Battle at the Binary Stars"
Georgiou notices that Saru has read and is familiar with Sun Tzu. Mirror Georgiou would notice this too, in the second season. So both Georgious studied his tactics.
Georgiou and Burnham -- the Captain and First Officer -- beaming over to the Klingon ship shows everything that's wrong with Landing Party procedures in the 23rd Century. Kirk was lucky enough to survive every time in TOS, but Georgiou wasn't. There are any number of times where Kirk could've just as easily ended up like Georgiou.
They managed to really bookend Burnham's time on the Shenzhou. From the time Burnham first came onboard and Georgiou hoped to mold her, to the end when Georgiou painfully realized Burnham wasn't ready to be the Captain she hoped she'd be and had misread her.
I think Georgiou misread Burnham because Burnham herself was confused. She was trying to be a Vulcan and, in reality, was trying to be something she's not. Georgiou was wrong about Burnham because Burnham was wrong about herself.
EDIT: Another thing I have to add is how much I liked the argument between Burnham and the computer when she was trying to get out of the brig to save her life.
At the end, the dramatic staged lighting when Burnham was sentenced was very spooky, somber, and delivered the tone they were going for. They need to take this type of dramatic license with the lighting more often. It was very effective. It sold the scene in ways that dialogue alone never would've. The darkness showed just how bleak everything looked and felt for Burnham with that sentence. Like the light shut off on her life.
Burnham was dead-convinced her life was effectively over. In the next episode, she discovered new meaning for it again.
"Context Is for Kings"
They really played up Lorca's mysteriousness. By the end of the episode, the first time I saw it, I thought, "This is one messed up Captain!" I couldn't wait to see what he had in mind next.
I loved when Lorca showed Burnham everything the Spore Drive had the potential to do. He sold Burnham on it.. and he sold
me on it. Even though Lorca's an evil bastard, he knows how to pitch something to someone.
After "Context Is for Kings", I'm glad Stamets dropped the "Who the Hell do you think you are?" attitude he had towards Burnham in this episode. It would've gotten old really fast, had it continued. Once Burnham shows that she can be a team player and really can bring something to the table, that's when he finally eases up on her. To the point where he hands Burnham a phaser to get the Tartigrade's attention when Landry refuses.
EDIT: I mentioned this before and I'll bring it up here too. Stamets reminds me of David Marcus in that he doesn't appreciate that his work has been co-opted by the military and he views himself a scientist first and foremost.
Tilly shows that she's willing to give anyone a chance is won't judge people based solely on their past. She's the only one who's willing to become friends with Burnham or not look down on her. Aside from Lorca, who thinks the ends justify the means and, like he said, "Rules are for lackeys. Context is for kings."
And in retrospect, it looks like Section 31 was involved with the Discovery's and Glenn's development from the beginning since we see those guards with what we now know are Section 31 badges. Looks like they left the ship when Lorca got the ship ready for active duty.
DOUBLE-EDIT: After the boneheaded choices Burnham made in "The Vulcan Hello" and "Battle at the Binary Stars", which she still feels guilt over, "Context Is for Kings" showed the other side of the equation. 1) When other inmates try to attack Burnham, she shows her physical ability to handle a fight. Vulcan martial arts. Even pacifists know how to defend themselves. 2) When Burnham is assigned to be a number-cruncher for Stamets, she shows how mentally adept she is by pointing errors she spotted in Stamets' work. 3) Burnham shows how she can think on her feet when they're up against the Tartigrade in the Glenn. These things all combine to show why she's the lead of the series. It shows how we don't need to have the Captain be the star of the series.
And with the Captain not being the star of the series, it allows them to go nuts with Lorca. He's not the main long-term focus or someone who show is telling us to look up to, so they're free to take him places where they couldn't with any previous Captain.
"The Butcher's Knife Cares Not for the Lambs Cry"
The supreme irony in this episode is when Voq says he doesn't want to use anything from the Shenzhou to power up his ship because he's obsessed with Klingon purity. And then, at the end of the episode, L'Rell sends him off to what we now know when be having him changed to become someone who looks like a human with that same human grafted onto him. So much for "purity".
Toward the end, when Discovery comes to the rescue of the colony, that was Discovery's Hero Moment. That's when it made the splash.
In retrospect: them showing off the Spore Drive and how they managed to get it working in these early episodes will pay off in the third season. I figure in the third season, whatever happened to the galaxy, Discovery's Spore Drive will become more important than ever.
And I have to had, this is the most unconventional Star Trek title ever.
EDIT: I have to add that when Lorca plays the audio from Corvan II, it shows how dire the situation really is there. And if Lorca were a normal Captain that would be it. But Lorca's not a normal Captain. So I think a little bit of it was also him using emotional blackmail to get the results he wanted, to show what the Spore Drive can really do.
DOUBLE-EDIT: One really Star Trek thing in this episode was showing that the Tartigrade isn't just what Lorca and Landry want it to be. We shouldn't judge a creature based on just its appearance. Simple enough message but one that too many people forget too often.
When Landry was killed off, I didn't see that coming at all when it happened. But in retrospect, I don't think she would've gelled with the rest of the crew post-Lorca had she stayed. She was too hardened and not just from the war. It would've been interesting to see some of her backstory, but it wasn't to be. More on her replacement when we get there.