I saw this today in the Dolby Cinema Theater set-up at the AMC 15 Century City -- it's been there for most of the year I gather, so now I'm kicking myself for not going there earlier. I had been seeing movies in their digital IMAX theater but I think this Dolby Theater is superior in every way. The black levels are amazing, like a film print.
The movie looked great. The ARRI anamorphics (and Greg's focus-pulling) were top-notch, I'd almost say that the ARRI anamorphics were almost too perfect... you got the stretched bokeh but none of the other artifacts of anamorphic, no flaring, etc. There was one shot of Spock (it's in the latest trailer) looking at some memorabilia and there is a horizontal anamorphic flare which I assume is some sort of streak filter. I also noticed that early shots on the Enterprise sets (particularly the bridge) had the slight halation from what looks like a #1/8 Black ProMist, which is what the J.J. Abrams movies did on the bridge set.
There may have been a subtle film look grain pass done to the Alexa image to make it closer to the look of the previous Trek movies, but like I said, it's subtle.
Nice LED lighting on the Enterprise sets.