I covered integration error in my first post here, point 3. The thing I was calling Box2D out for is the fact that it doesn't use a hacky way of rectifying collisions. It seeks out the point in time that they occur.

>It does not guarantee zero error: to do that you have to have an analytic method, which isn't applicable to a general-purpose physics simulation.

If you have constant acceleration, the analytic way to get the point you want to be at at the end of the frame is simple: just pretend your current frame is using half the added speed from the acceleration that you're going to undergo this frame. Or you could use a hermite curve or something.