Disclosure: I have read the source manga up to the current series and have also seen the anime. As such, there may be bias, unconscious or not in this review.
Personally, I loved the movie from start to finish. Can't imagine the BD being different. The visuals are stunning, a true credit to the talents at WETA. The acting is solid and Rosa Salazar's motion performance from body to expression are captured perfectly. Alita, in my opinion, comes across as a living being among the rest of the cast. Being fair, other mocapped actors did great jobs as well (Skrein). Rosa’s performance truly separated Alita from the others though and she deserves some kind of award recognizing her work in this movie. This film should also win visual effects next year (I doubt anything will come close even in the next 10 months). The action is thrilling, well-choreographed and never dull with some serious “owns.” The film adaptation is ambitious, taking a few volumes of the manga (which is a very rich universe) and mixing it with elements of the anime, then fitting it into two hours...there was easily enough for a 2.5 to 3 hr movie. I do think some aspects, especially Japanese symbolism, may be lost and/or misinterpreted through a Western lens. Kudos to Rodriguez’s and Cameron’s execution of this movie.
Is it perfect? No! I found some dialogue cheesy and there are two nagging questions I have from the manga that persist into the film. However, while there, the minor flaws did little to detract my enjoyment of the parallels and contrasts in characters, off the hook action and some genuinely emotional scenes (for me at least). While not heavily advertised, and the disparity of critic reviews versus audience reviews being so stark, the movie is worth it. Great movie!