This post will have less content than usual, so I'll try to keep it short. This post is mostly here to jog my memory if I look at it in the future.
One of my interests is in how heterogeneity has important effects on aggregate economic variables that get lost with the "representative agent" framework. One somewhat-well known example is borrowing constraints; if they bind different agents differently those agents may behave, in aggregate, in a way that is very different from how any single agent might be expected to behave. There's a lot of literature on the idea that many of the homebuyers driving the recent housing price bubble were, in fact, acting at the time they did in part because they had recently had borrowing constraints eased. Other agents may, in this sort of model, still play a role in magnifying what might be a small bubble if it were left only to the agents whose borrowing constraint was loosened; agents bid up prices in anticipation of each other. Depending on the response functions, you may only need a small initial impetus to cause a dramatic change. (The multiplier may even be locally infinite in some sense where you have a no-longer stable equilibrium.)