Overall, I rather liked it. I will say, however,I was somewhat surprised by the fact that while the movie focuses on the clash of new and old methods in regard to music, they don't even remotely touch upon the idea in filmmaking. You'd think that for such a significant theme and parallel between the two character's career paths that it would've been touched upon more. Oh well.
Uh, what? they use matte paintings and camera tricks with miniatures and cutouts, which is all classic film techniques. Not sure what you're getting at.
Have you never seen singin' in the rain? The post-party tap sequence is play by play classic musical.
Same with the scene in the observatory. Hell, they even recreate a shot from rebel without a cause.
This is all paralleled with it being set in modern day.. the opening two sequences are very 'modern' filmmaking, too. Large crane shots, elaborate scene changes, etc.
Any song/dance number that involved the two of them together was very 'classic hollywood', and any solo number was more modern stylistically. Keep an eye out for that on your next rewatch.