I have two Jazzmasters, one of the '62 AVRI models and an early 90's Japanese made model. Both are great and super playable, the Japanese one has a noticeably slimmer carve to the neck. The AVRI has a rounder shape, still fairly slim, the Japanese version is slimmer and flatter.
No, it's no problem. The Japanese guitars are absolutely great, and if I had to pick one of the two Jazzmasters I own it would be the Japanese made one. I've had it for twenty years now, and intend to have it when I die. The playability on the things is staggering. Great guitars. But I'm very sentimental about that one. I learned how to play guitar on it, how to express myself.