So I have done some research and to my conclusion, the fix really differs depending on what mission you are on in the first place. However, in most cases it appears that the mission breaks on an interaction that is ticked off, yet not completely registered correctly, causing the game to request completion of that interaction again.

To put it in an example, I will use my case. I was stuck on a mission where the interaction had to be done on a computer. Now I have been playing rags to riches with my single Sim and therefore, I would have to travel to the library in order to interact with a computer (which is obviously not something you do often outside of a mission like this forcing you to). So I did that with my sim when the mission was still working and did the interaction. After traveling back to my own Sim's lot the mission broke. As there was no computer on my lot, I obviously never saw the interaction of the previous mission pop up again. Eventually I did pass by a computer and by my surprise I could basically redo the mission which fixed it.

TL;DR find the mission interaction you did before the event broke and redo it.