Got my first offset guitar a couple weeks ago. Squier Classic Vibe Jazzmaster in Olympic White. Very impressed so far with the quality. Everything on it is nearly perfect except for the output jack (easy fix) and the tremolo, which put it out of tune with even the mildest use.
Following standard procedures I shimmed the neck, raised the bridge, installed some 11s and filed the nut slots accordingly. Played and sounded great after that, but the tremolo was still completely unusable.
I took it apart and found the problem to be the square end of the fulcrum plate (is that what we call it?) wasn't able to sit properly in the groove so it couldn't return to it's original position.
I took the plate out and filed it down to a near knife edge and polished the edge a bit, and then put it back together with a little bit of grease on the end. Worked perfectly after that, stayed almost perfectly in tune even if I dive-bombed the trem. With that fix its a pretty awesome guitar.