People need to understand rounding better, especially the topic of when rounding can happen and when it can't for the basic operations.

Updating with a concrete example: The Fortran standard defines the real MOD and MODULO intrinsic functions as being equivalent to the straightforward sequence of a division, conversion to integer, multiplication, and subtraction. This formula can round, obviously. But MOD can be (and thus should be) implemented exactly by other means, and most Fortran compilers do so instead. This leaves Fortran implementors in a bit of a pickle -- conform to the standard, or produce good results?

Definitely. People think they'll get out of knowing how rounding works by using arbitrary precision arithmetic, but arguably it's even more important there (you run out of precision/memory at some point; what do you think happens then?). You can use floats for money if you do the rounding right.