I've just finished installing Linux Mint as a dual boot on my third PC (for experimental purposes) and was trying to figure out how to remove the password, or at least to stop the system from asking for it at every step, which is very annoying.
I found this Linux Mint forum and was quite shocked at the arrogance of the replies, not to mention the rudeness.
Anyway, the way to do it is by:
scroll to bottom
<username> ALL=(ALL) NOPASSWD: ALL
CTRL+X TO SAVE
Hit Y then enter
This stops the password prompts every time you want to do some admin work.