Text Appearing Wavy/Distorted in InDesign and Exported Files

I guess you're referring to the slight differences in some letter heights (notably, D and C in the screenshots below).

I don't have an explanation, but I wonder if this distortion occurs only at certain font sizes? For example, when you exceed a certain size?

(JPEG pixelation is a different issue addressed by @James Gifford—NitroPress ).

What's the resolution of the exported JPEG — about how many pixels high are those letters?

Some fonts just don't scale down to middling pixel-based resolution very well, typically older/classic faces designed for solid type. (That's the main reason for most of the "modern" faces in common use  — they were designed for digital reproduction and don't get the wobbles and shivers when pixelated in an image or on screen.)