I don't buy that. The errors in the ads need to be obvious errors in order to fit with the gag style of the play, not a simple misstatement of fact meant to help sell tickets. This is a play that's now Off Broadway that's trying to confuse potential buyers into thinking it's on Broadway. No two ways about it.
I think the idea isn't that it's the longest-running Broadway play in history, but that it's currently the longest running. But it's not on Broadway, so it's wrong.