First, have you checked the blade? A poor quality blade or one that has gotten too hot can easily warp enough edge to edge to cause that kind of movement.
Second, Pull the blade and make sure the shaft surface behind the blade is clean. Doesn't take much of a piece of debris caught back there when changing blades to give you all kinds of wobble.
Third, once you reseat the blade and tighten it down, grab the top of the blade carefully and try to wiggle the blade side to side. If the blade and shaft move side to side slightly, but together and level, no problem. If the blade seems to "wobble" you have bearing issues and a new saw might be the answer.
I always check the cheap stuff first before I go looking at new tools.
