Does it also sometimes register a double click when she means to single click?

I have a few different Logitech mice, all of the same model (Logitech Anywhere Mouse MX), and all of them developed noisy primary buttons after a few months.

The symptom was that any time you clicked the button it would randomly be a quick sequence of a random number of clicks. And if you were holding down the button for a drag operation (such as selecting text) it would randomly act like you had quickly released and then re-held the button at random points during the drag operation. That could easily explain the behavior you were seeing.

Other than a new mouse, my fix was to actually desolder the buttons from the pcb, dismantle them carefully, scrape the contacts clean, reassemble and resolder. Found an instructional page online of a guy doing it to his Logitech mouse.