Have an option to dis/enable this display categories feature. Option is off by default, so the calendar continues operating just as it does now. (Not sure if that option could be in the "screen options" at the top of the calendar's display, or if that has to somewhere away in a true settings area.) Then, if it's on . . .
Compose a distinct marker for each category. (I'm thinking something you can whip up within the calendar's display code -- not something that you have add as a feature/option on each category.) Take the first letter of each category; If you get to a category and the first letter was already seen, then use the second letter. (or maybe you only use consonants.)
So we have "N" for my "news" category, "P" for my "parsnips" category, and "E", (second letter,) or "L", (if using next available consonant,) for my "people" category. Each post's category letters are added to the display; I'm thinking between the time and the title. I'd prefer the markers presented with a little color-filled box around the letter. Just pick a pallette of muted colors that are simply assigned in order to the markers. (Maybe an option for 'use colors' versus 'use gray shades'.)
Now I can view 8 weeks at a time... and I can see "N", "P" and "E" posts. At a glance I can even see how much red (eg, if N's are on a red-filled little box), how much blue ("P"), etc. So I can get a feel for the categorical balance of what's going on in my calendar.
If people have too many categories on each post, (in their opinion when they flip the option on,) it will be a mess. So for such use cases can just leave the option off -- they don't have the feature as-is anyway. I think many use cases though have one or two categories per post.
UNRELATED: ¿ An option to limit the lengths of the titles displayed ? Just a "truncate titles" to a specified number of characters. That would let the power users save some space. too.