Many of the events are recurring daily or weekly but are only interesting to the user once.
This spiral plot example is used for historical data, but the general idea might be adaptable..?
Small Icons (e.g. color+symbol) for these events, that are listed either in a separate list outside of the calendar, or within the calendar, but only once.
Mousing over one of the icons could highlight all icons of the same event, so that the repetition pattern can be spotted easily.
suggestion, a button that 'fades' the recurring appointments to a light pastel (or similar) and keeps the unique appointments with full saturation. All hover and click functionality should remain, but a 'highlight only unique appointments' button would be a good idea (though I'd hope you find a smaller name/description).