I'm nearly sure that this is only solvable by replacement of the device but I'd like to vent the issue.
About 9 months ago i got a nice Logitech M705 mouse. which inspired me to add paging via scroll wheel to my mupdf and now i think i wouldn't like it any other way. well, back to the present.
The symptoms are that the left mouse button can't be held down. It'll emit multiple button release and press events when pressed down and more when released. This makes drag and drop impossible. I've opened the mouse and verified that it has the same problem even when the actual button is pressed by hand and that it's not due to any damage nor dirt. What's funny is that the scroll wheel and the right button work as they should producing only one press event when pressed and one release event when released.
Due to that I know that it isn't a problem with anything in my computer as if it was you'd think it would effect the right mouse button too. And it's not a problem with the wireless as the mouse tracks nicely (although it doesn't track as good on worn particle board which is uneven do to water exposure as this Logitech M-UR69 but that's a wired usb mouse).
And I can see the extra button events using xev
these only appear when the left button is pressed but not the right for that it gives the perfect response of one press event when pressed and one release event when released.
So if its not my laptop nor the wireless and it doesn't effect the right button or the wheel nor the tracking, it must be that i broke in some weird way the left mouse button's switch.
I did find that some one else had this issue with this mouse:
I've recently encountered problems with the left mouse button not staying closed when I hold it down. Trying to drag things across the screen becomes a major malfunction when the button lets go and I have no idea where the icon was just dropped. Taking the mouse apart and blowing it out thoroughly seemed to resolve the issue but why did I need to do that to a six month old mouse in the first place? And how long before the problem comes back?
From http://reviews.logitech.com/7061/5843/logitech-marathon-mouse-m705-reviews/reviews.htm
That's what made me think that it could have been a dirt issue, but I didn't find that helped.