How do SC justices consider the factual basis of litigation, rather than issues of law, in appellate review?

Question

What consideration do United States Supreme Court justices give to the factual basis of litigation, rather than issues of law, when considering appellate review? Also, how can this relate to the writ of habeus corpus?

In regards to "factual basis of litigation" and appellate review only looking at the record of court proceedings, I mean what consideration is given to the facts of the case--rather than issues of procedural law.

Answer 1

They can ONLY look at what is contained "In The Record." This means that NO NEW EVIDENCE can be introduced. If there IS new evidence, they can remand for a new trial.