Solids have a type of osillation which is longitudinal but, strictly speaking, is not "pogo", which is a characteristic of fuel slosh affecting the turbopumps, in turn affecting the thrust level, such that as the turbopumps start to spin up or down to compensate they act in phase to reinforce the oscillation. (I think, someone correct me if I'm wrong)
As for the max size of a booster, think of it this way: what's the max size for a skyscraper? Take that and imagine filling it with liquid and thrusting it into space, and you realize you will have to make it smaller to start with. Obviously there are limits based on the limits of the construction materials.
When you say "theoretical" you have to specify what's included in your theory. Using pure rocket science math, there is no theoretical limit. You just add more fuel and more thrust. But if you take materials into account, limits pop up quickly and the problem becomes much more complicated. No one knows for sure how big a building we can build; we're still learning and some people even think a space elevator is possible. Certainly we don't know for sure the exact size limit for a rocket.