If you're talking about sections of the plot or segments of the story, you might look at a phrase like story arcs or plot arcs (the part where he's investigating before he finds what he needs to act, the bit where she's talking with someone before the story shifts, what's happening over the course of the party scene).
The phrase story arc can be used to talk about subdivisions in a story, or development of a plot over a longer timespan (several books or episodes). Narrative arc is another phrase, sometimes contrasted with the larger meaning of story arc - specifically smaller episodes if there is an overarching story, and sometimes used similarly to the smaller sense, to track the plot by often standard constructions. Plot arcs, is another version of the phrase.
These kinds of divisions work better with significant chunks of story-line, or the development of the whole of a subplot, rather than individual events - or it can be used to talk about the development that happened between significant events (minor plot event happened during the plot arc between...). Character arcs can also be used to talk about the development of a character, and their specific storyline or subplot, over the course of a larger work. Mini arcs might be used to show smaller segments of a story, events where things happen but on a smaller scale, even on a scene by scene basis. Subplots can act similarly, but involving small, almost separate plots interwoven through a larger work, rather than an episodic segment or scene of that work.
If you're talking about specific events, then Yitzchok's suggestion of plot element will work for smaller points, and MyLifeisanAbyss's suggestion of plot points works for more significant happenings. You might also try using just 'points' as an alternate to event for something that happens but need not be significant - the story had a point where (X), that point in which (Y), and Y happened at the other point. This will sidestep the way 'plot point' tends to be used for turning points more so than every separate happening in a story.