surely saying "it's a common problem" is more realistic than saying "it's a well-known/famous
To say "well-known problem" does sound kind of strange, but it could be possible under certain circumstances. "Well-known issue" is a better collocation in English. I think the translation here is simply showing that the Russian word известный can be translated as well-known.
Being a computer scientist, I agree:
"The list below contains some well-known problems that are NP-complete when expressed as decision problems."
I take notice though of the native speakers comment that "Well-known issue" might be more natural when the problems are not mathematical in nature but a "real world issue".