Shot by shot, here's what I think:
1. Boyega popping up in the desert:
This feels like the OT to me. The desert is quite evocative of the OT Tatooine, and feels right. The best part of this shot is that Boyega is wearing real armour, and it looks like he's been wearing it. There's sweat and dirt on his back and chest, and there's sand stuck in the ridges of the black under-armour. That's the kind of used universe feel I was hoping to see.
2. Soccerball droid:
While this was probably my least favourite part of the teaser, that droid definitely felt like a Star Wars droid, in a Star Wars environment. Its means of locomotion seems a little odd, but perhaps it's more efficient/economic to make them that way. It does seem to get around faster than most other droids that don't fly around (Droidekas being a notable exception), so maybe that's why they're made that way. If this ends up being the most ridiculous thing in the movie, then I'll be quite happy.
3. Chrome troopers:
The blue tint was a bit obvious in this shot, and I hope the movie is better colour-timed. I still like the design of the troopers. I have little else to say about this shot.
4. Daisy Ridley flying away from something:
I rather liked the speeder design. It gives off a strong OT vibe, but is original at the same time. We can also see the little gate thing we saw before in (intentionally?) leaked concept art, which continues the pattern of leaked things being what shows up in the teaser. This shot also had a used universe feel and Ridley's outfit seemed to fit with the kind of Tatooinian garments we saw in the OT (I think).
5. Cockpit shot:
Again, things look used. The helmet has chips and scratches, the jacket is slightly worn, the paint on the corners of the metal box-thingys behind the pilot is worn off, the edges of the windows look like proper window edges, etc. As has been pointed out, the guy's face has some character. He isn't wearing perfect make-up in this shot. Overall, it feels very authentic.
6. X-Wing flyby:
Again, I really enjoyed seeing stuff from the OT, but updated. This is my favourite shot out of the whole teaser. It's neat to see familiar spaceships outside of empty space or a hanger bay. And again, the ships don't look shiny and new. That alone has me feeling optimistic. The used universe feel is something I thought important about the OT, and it seems to be here. We just have to get used to seeing it in a modern-looking movie.
7. Monk with wounded leg in snowy woods:
I have mixed feelings about this one. On the one hand, it feels kind of mysterious and cool, but on the other, it looks like there might end up being a Sith in this movie (is it possible this is the Inquisitor from Rebels?). I wasn't sure about the lightsabre at first. It seems like they tried too hard to be cool with it. I like the interesting flickering blade, however, and lightsabre designs don't really bother me that much. I'm quite happy with there being variety. The possible presence of Sith is what I'm less enthusiastic about.
8. That ship that Lando flies in RotJ flying around:
The Millenium Falcon felt like it had some weight in this shot. I could almost feel the g-forces as it flew around and did some crazy stunts (is ancient old Han still the one flying this thing?!). It does look kind of thin to me, but I don't really care. It wasn't scaled properly within the OT either. The TIE Fighters look too similar to what we saw in the OT, but I can't say I got a very good look at them. Hopefully these aren't new fighters they're still making the same way as 30 years ago.
Now that I've gone through the teaser shot by shot and analyzed it, I'm far happier with it than I was before. There are some things that really feel like Star Wars. Others, not so much, but I can't say I want everything to look like the OT. I'm all for moving the camera around if it improves the shot, like it did in the one with the Falcon. I like that I'm seeing a used universe. Let's hope it's consistent. The trailer hasn't got me riled up and eager to see the film, however. I am no more or less interested and excited than I was before. I'll continue with my wait and see attitude, until I actually do see.