How do schools have the same number of each week day? My school is currently on a 14 week schedule where we're supposed to have 14 Mondays, 14 Tuesdays, etc. each semester.  Because of various holidays, that's harder than it sounds, and so we have a couple days that have to get adjusted; for instance, tomorrow is a calendrical Wednesday, but an academic Monday.

This has some drawbacks: some students have outside commitments (for instance, jobs) which don't shift just because our schedule does, and because the modified days always happen on short weeks, compliance is limited.  (For instance, it's already hard enough to get students to stay around for classes on the Wednesday before Thanksgiving, but it's really hard to get students who have class on Friday to realize when they make Thanksgiving plans that Friday classes meet on the Wednesday before Thanksgiving.)

How do other institutions deal with this, and are there any particularly good solutions to it?
Make up days at the end of semester

The solution that I saw used is that for certain subjects, where one of "their" days fell on a holiday, the semester was one week longer, i.e. the break was shorter. Your described solution was not considered feasible - transferring a Friday class to Wednesday would fail because (a) there would be some students who have also chosen the Wednesday class and would have to be in two places at once; (b) there might be also a similar collision for lecturers who teach multiple classes and (c) there weren't enough facilities to host all the usual Wednesday classes plus all the usual Friday classes at once.

Skip them

Another reasonable possibility is to reduce the number of lectures. If it's known well in advance, it's no problem for a lecturer to take a course that usually is split in 14 lectures and teach it in 13 - and they can shift part of that material to extra reading and homework in the "empty" week where the lecture doesn't happen but students do have the rest of the week available.