The most alarming possibility is pre-stall buffet.......... which presumably would have operated the stick shaker (which would NOT cause the vibration!) , which would be recorded on the FDR / FLIDRAS (?)
Rotate at too low a speed and you're either going to scrape the tail as it struggles to get airborne or if it does, by definition, your going to be right on the limits of the available lift. Wrong numbers punched into the FMC and/or incorrect weights have resulted in accidents before.
I don't know, I wasn't there etc etc......
A4