It's really speculation as to what each individual citizen thinks. After the Purple Wedding, I believe the opinions of Ned might have changed for some, having had to live thru the child king and Cersei's rule.
Enemies of the starks will look at him as either a traitor or less than nothing.
Friends of the starks would ignore anything they heard in the negative and would just flat out refuse to believe he was a traitor in any way.
The other neutral nobles might form their opinion based on facts. Littlefinger and Varys both knew Ned was a good guy but stupid. It would be a safe assumption a lot of others would feel the same way.
The commonfolk who didn't know him, would either form their opinion on either of the above, or on stories they hear.
The play is the most telling because it shows us how a good chunk of the world might view the situation. It poked fun at his rigid personality and lack of intelligence. It's possible most of the populous would view Ned as an honorable fool.