I had the same thing happen to me in the beginning. I think that the edge of the record was binding a bit on the edge of the slot, but not sure. Anyway, the problem seemed to work itself out. I have about 300 records "in the bag" and it doesn't bind at all anymore.
I did notice that the unit doesn't want you pushing down on the record when you place it in the slot...simply set it in and push the button. Secondly, the instructions call for you to rotate the record slightly counter-clockwise once the record is set. You will find that this procedure works wonders if the slight rotation is performed immediately after the brush heads initially move into the record to measure its thickness. Those heads then move away for several seconds. if you can slightly rotate the record then, you will find that it almost never has problems.
I have had 2 records that had issues with reliably rotating. The thing I noticed about both were: they both had very "sharp" edges and were "cheap" records and both were dished. I think that the dishing may confuse the thickness detection routine causing too large of a gap and insufficient traction to turn the record.