They aren't "out of sync". Aside from Rex (who performed his songs live on the set), it's just the usual 'slightly rubbery' effect that happens when somebody is mouthing to an audio track. The movie has always had this.
Yes, I would have included Dame Wendy Hiller but I was mainly just concentrating on the musical Eliza's. Ten points to the person who can identify all of the ones I featured in the collage. ;)
I want the extras, but I may hold off to see if Paramount here in Australia decides to release this later in 2016 - perhaps to tie in with the 60th Anniversary production of the musical directed by Dame Julie.