Workaround: mark the media as watched at the lowest level you're comfortable with. For movies, there's only one level. For series, you can mark the episode as complete, the season as complete, or the series as complete.
If you don't want to record that you've watched the media, mark it as unwatched immediately after. This discards your progress and ensures that "Next Up" doesn't populate with the next episode (or next season's first episode). Unsure how it interacts with systems like Trakt if you run those, but it works as a general solution.
It is not the problem with single Episodes or Movies, but with entire Shows i don't like to watch anymore at this point, but don't want to loose the "progress".
A simple "Drop/Dropped" option, that hides it from the view. Can be on the highest level of the database show entry as boolean and should be pretty easy to implement.
Not necessary, but nice could be a filter for this dropped series.
I would provide it myself, but don't have much time at the moment and would have to familiarize myself first.
I'd already be grateful if (for stuff like the multiples mentioned above), there would be a way to nuke all older entries and only keep the one furthest ahead.