What's even more interesting about this particular mistake (at least to me) is that it often shows up as hypercorrection[1] by educated, fluent speakers of English who've been socialized to recognize "You and me" as the subject of a sentence as wrong, and perhaps as ignorant-sounding, but have formed a too-aggressive (wrong) representation of the underlying rule.

Basically, I know a bunch of people who've been to college and would jump right down your throat if they hear you say "You and me should grab coffee some time," but will walk around all day saying things like "Hey, let's see if Fred wants to grab coffee with you and I."

[1] https://en.wikipedia.org/wiki/Hypercorrection#Personal_prono...