I imagine if you zoom in far enough on those points you have the acceleration continuously changing as pressure slowly builds in the engines over several microseconds.
There is an interesting Δa/Δt while fuel is consumed and mass changes.
There are discontinuities to the graph when engines are shut down and stages decoupled.
Over a macro scale, it’s discontinuous, of course.
But, checkout Zeno's paradox for more on your philosophical questions