Those are less problematic than you might imagine.

- For language, individual words might be discrete, but concepts being communicated have more nuance and fill in the gaps.

- For language, even to the extent that discreteness applies, you can treat the data as being sampled from a coarser manifold and still extract a lot of meaningful structure.

- Images of cars are more continuous than you might imagine because of hue differences induced by time of day, camera lens, shadows, etc.

- Images of cars are potentially smooth even when considering shape and color discontinuities. Manifolds don't have to be globally connected. Local differentiability is usually the thing people are looking for in practical applications.