I had no wobbles that I can remember. The clamps on the side held the machine firmly, and I don't recall every having any problems. I really liked that carriage, way better than any of the wooden ones I saw, though I never used a wooden one. The handles were attached firmly and I had no trouble guiding the machine, either FMQ or ruler work.
I had the Bailey with the Grace frame for a few years and then upgraded to an HQ Fusion.