In "Software & Updates - Updates" all look un-checked. But I know they are in fact all enabled:
When trying to check them, I cannot, as they are immediately un-checked.
It looks like so:
For higher detail see this video. (The problem on the update errors reported along with the video on elementary Google+ and also present at the beginning at the video is now outdated/solved; I am referring to what happens after 0:15.)
What happens in fact is that each click there creates a duplicate (for the recommended, unsupported and important updates) in "Software & Updates - Other software".
I have solved this just by removing those sources added there in this way so that only one entry is left there for each type.
After that, all updates and sources are fine. But the problem with the "Software & Updates - Updates" check-boxes is still there.
Those check-boxes under "Software & Updates - Updates" still looks un-checked and I have to avoid touching them.