I dont think its lip sync... Can someone vouch for it? My dad was/is a die-hard Beatles fan, and hes dead set that its them singing.
Not out to prove him wrong, just curious.

Doesn't look lip-sync'd to me. Definitely not a version I have heard on a recording before, and I have listened to this song a lot with several different variations (the single is different from the version on the album, and I seem to remember once hearing a third version even).

I heard a flub on the organ and a tiny bit of feedback at one point, but what 'wrong chord on the piano' are they talking about?

I'm pretty sure this is taken directly from the documentary film "Let it Be", in which they are shown performing many songs which were actually recorded for release at a different time (though perhaps during this same session). I seem to remember that there is footage in that film of some performances which sound like they may have actually been the recorded takes that made it to the album (or single) and many others which definitely were not (Octopuses Garden comes to mind). To watch the entire movie, there is little to suggest that any of it was lip-synched. There wasn't really any reason to do so - the ad hoc "roughness" was the style of the movie, and viewing it certainly leads one to believe that no effort was made to polish it up at all.

...and Geist is right, the singe and album versions had different guitar solos by George and different keyboard solos by Billy Preston there. Neither was this version.

Good job in the modified description, Jaxon. Thanks for the research.

Perhaps I just confused the lip synching with the apparent apathy in John's and George's look on their faces.