-- Why wasn't Stamets more aware of what was going on with the Glenn? Wasn't he partners with the lead scientist on that vessel? It seems like they should have been in some form of communication...
-- Why do we have no sense of the relationship between Captain and First Officer yet? It's weird to me that the relationship of Saru and Lorca is such a blank. I have no sense of how they relate to each other -- Trek has always made such a big deal about captain's selection of first officer, and I have no clue why Lorca would pick Saru, they seem like such a terrible match.
-- Tilly, A CADET, steals a bunch of highly classified spores and takes them to Burnham. It all turned out fine, but that seemed like a pretty extreme action to just gloss over so quickly, especially from someone of her rank.
-- And the sarcophagus ship Klingons have just been hanging out in the same spot for 6 months? That was such an awkward way to pause their narrative, while SO MUCH else has gone on with all our other characters...
- The Glenn: Starfleet separated the two spore drive creators to get two independent lines of research working. So if one team gets stuck, the other team won't necessarily because it has been taking an entirely different approach. Stamets friend from the Glenn was only telling him generalities because he wasn't allowed to disclose specifics.
- CO/XO relationship: This series is being told from a non-captain/non-senior officer perspective. We aren't supposed to know everything about what is going on - kinda like actually being a crewman on such a ship. Secondly, Lorca keeps himself a mystery to a lot of the crew. Third, Lorca hinted at why he has Saru as XO, for the opposite reason he has Burnham onboard. Where Burnham will make those intuitive leaps, violating orders if neccessary, to get the job done, Lorca has no wish for that from his XO. Saru is a by the book kind of guy who won't buck Lorca's commands.
- Tilly: like the rest of hte crew, Lorca expects everyone to do their best and get him his results. He likely knows that Tilly took the spores (just as he knew Burnham broke in to the spore bay), and its fine as long as it is advancing the mission. Heck, he probably would ahve been just fine with it if either Burnham or Tilly had just requested permission - as long as it was advancing his agenda.
- The Klingons: agreed it was awkward that it took them exactly 6 months to get moving again.
...1. Why did they rescue the telescope and leave the ship? Ditto the Klingons leaving T'Kumva's ship. For 6 months. Rally around him & start a war? Yep. Leave his followers to starve & abandon the only ship you have with a cloak for 6 months? Silly. Ditto Starfleet. You went back for the Telescope but left the Klingon flagship? Take it & try to undetstand the cloak. This was beyond stupid...
The telescope: Saru or someone else likely took it along as important to the Captain as they were evacuating the ship. Since it was a family heirloom, which Saru probably knew, he knew it should be returned to Georgiou's family. Starfleet didn't return to get it.
The 6 month pause: I think Starfleet didn't return to the system because they had to evacuate the system because of the immediate attack of the Klingons en mass all along the Klingon border. Less understandable is the Klingon's failure to return sooner. They obviously can return (though maybe, maybe, there was something else that was holding them back until now?), and they should have made it a high priority with the cloaking device so important.