My mouse's left button was behaving inconsistently. Sometimes I would need to click two times or press harder before the command got through. It was time to get out the scalpel and open it up!
I couldn't immediately find an obvious way to open up the mouse and was already reaching for a screw driver to try and pry it open when I luckily remembered to reach for the internet first. Somebody, somewhere, sometime must have tried to open up a similar mouse before and left a trace about it on the net.
So searching for "Dell MS111-P mouse repair" quickly brought me to this video: https://www.youtube.com/watch?v=LiKUuDCPIfk
Seems that under the big PTFE mouse skate is a regular screw. No need to pry open anything! I didn't pull of the complete skate as I put it back in place once I removed the screw so it wouldn't get full of dust.
Once you remove the screw, opening it up is pretty straight forward.
When open I could immediately see that some dust had collected inside and some hairs and dirt were tangled up around the scroll wheel.
I removed the scroll wheel and got my brush and cleaned out the interior.
When all dirt was removed I sprayed some contact cleaner in the switches and the rotary encoder of the scroll wheel. (If you don't have contact cleaner some WD40 or a very small amount of white vinegar should do the trick also)
Mind that I didn't unplug the mouse as I wanted to test immediately if my actions had an impact, so special care was needed to avoid making any short circuits.
When I wanted to close up the mouse I noticed that it was possible that some dirt would get stuck between the plastic of the mouse housing and between the moving plastic of the button on top. Maybe some dirt here was hampering the correct functioning of the button? So, for good measure, I took a strip of carton and ran it between the two parts to make sure nothing was stuck in there.
I closed it back up and it has been working without problems ever since. I hope this has been useful for you and it can help you in keeping your mouse alive.