I picked up one of these a couple weeks ago too and while the sound quality has been fantastic I had the same issue with the puck not sitting all the way down and the player having issues reading maybe 10% of discs.
The comments here got me to look a little closer at the puck and the mechanism and I realized the puck requires a small amount of pressure to kinda click into place. Mine didn't take much but I was so used to other players that don't click in place I never tried it. I'm not sure if this is by design or just poor tolerance on the manufacturing of the puck but after placing it correctly the discs that couldn't be read before now work fine.
I had been expecting to have to send the player back so this makes me very happy as this thing sounds amazing.