To preface this post, I'll start of by saying that I've really enjoyed my time with Star Trek Discovery so far.
The first two episodes feel like much more like a lead-in movie than the first two episodes of the show. They don't feature the titular ship at all, for example. They're obviously intended to be a double feature with a stunning hundred ship battle as the conclusion, though there is some tidying up at the end. The Klingon war-rhetoric did get a little tired by the end of the two episodes, but it wasn't enough to be offputting.
There were some inconsistencies with the background to the show. It felt weird that the Klingon leader stated that "we come in peace" is the federations battle cry, given that they haven't encountered one another often. On top of that, Michaels family was killed by Klingons, but at another point, we're told that the federation hasn't seen the Klingons at all for 100 years. I'm sure it works out - it just felt inconsistent.
As much as I enjoyed the episodes, I also had some concerns about how the rest of the series would be with them as an opening. Luckily, episode 3 changes the pace almost completely. The war that started in the first two episodes is no longer the focus, merely background noise to add emphasis to what they're doing outside of it. We're no longer in the middle of the war - we're now on a scientific mission, and we even respond to the distress call of another ship out in space. It felt a lot more like Star Trek. I'm looking forward to the rest of the series a lot more now than I was this time last week.
That said, I still don't particularly care for the show being a prequel to TOS. Why can't we just have a 'new' show. I also don't care for Michael, the main character, being adopted by Sarek. I don't mind that she, a human, was raised on Vulcan. I don't mind that she went to their school. Her being raised by Sarek feels like a weird retcon that could have just... not been.