I am having the same issue. The house is in Island Paradise. This is a stackable unit. I am not sure, if this occurs with the non stackable units. The sim starts the laundry and then the laundry seams to finish (or not). There is no visible laundry in the machine. Then all interactions with laundry machine disappear. I can't do laundry again. The only option that is visible is upgrade, but when I try to click on it it says that the machine is not available (as if laundry was in it). Like I said no laundry is visible. The machine becomes unusable and hamper gets filled. No interactions with hamper are available. The house fills with dirty laundry. I have seen this complaint before and it said it is fixed. It is not. I replaced the machine 3 times and after 1-2 washes it happens again. The only thing that fixes it is getting a new unit every wash. I would hardly call that a solution. I do not use mods or cc. This game is boring without them (it's vanilla pudding, perpetually happy, no story progression, glitchy snoozer. That is a different complaint though), but I have to replace, disable or remove any mods any time something is not working, which is every time I play.
Ps: I just saw your laundry list of glitches. It is baffling how showering in the rain takes precedence over cancellation of assigned tasks (which my sims do all the time making this game nearly unplayable) and inappropriate sim action (pushups during weddings etc.) or simulation lag. Sims 3 had an open neighborhood that created lag and crashing to desktop, but without open neighborhood this game should work better, but instead beats it in glitches by a mile.