The train of thought that led me to this question is that I think most judges are well read individuals with an interest in public affairs, so when there's a high profile case involving a well-known public figure, it's easy for me to imagine that they might have a lot of pre-existing knowledge of the individual, and wondering if that has ever come into play in a case. My understanding is that judges are required to recuse themselves if they have a *personal* involvement in the case, but I've never known what the line is for impersonal public knowledge. Is a Judge allowed to introduce something that they have reason to believe is relevant to the case if neither side presents it?
Broadening our scope a bit, can a judge step in if someone gets basic facts wrong? If I'm being sued by someone claiming my product causes cancer, and I bring in an expert to testify to the safety of my products who says something like "cancer isn't real, it's purely psychosomatic, you can cure it with thinking real hard," and the defense doesn't try to impeach or challenge his testimony for some reason, can the Judge say "actually, sorry counsel, that expert is a crackpot, I'm not accepting their testimony, find someone else"? What would the limit be for doing something like that?