The first scene was one of the coolest scenes I've ever... seen.
Not only do they introduce you to Baby, the coolest fucking dude on screen since James Dean, but it has one of the best car chase scenes I can remember and that SOUND MIXING. Which brings me to my next point...
THAT SOUND MIXING! Will be nominated for all sound-related Oscar, and I would imagine it will be a serious contender in any given category.
Speaking of sound, I thought the soundtrack was excellent. At first it reminded me of Guardians of the Galaxy in how important the music was to the protagonist and how it was both diagetic and non-diagetic, but I think that Baby Driver actually did it better. At the very least, the music is a far more interesting mix. Guardians soundtrack was great, but after a while it's like, "Here's another second tier 70s favorite!" where Baby Driver had a very nice mix of genres and time periods.
All the acting was fantastic, but if I had to rate the main characters in terms of how much they crushed it, the order would be: Lily James, Jon Hamm, Kevin Spacey, Jamie Foxx, Ansel Egort
And last thing I'm going to gush about for now: When Jon Berenthal says,
"And if you never see me again, well it just means I'm dead." I knew as soon as he said that we weren't seeing him again, and I thought that was hilarious. I'd think back to it at various times during the movie and just start laughing. I wonder if there's any confirmation hiding somewhere in the movie that he got killed.