Renaming video files based on episode title lookup
Looks good; there's nothing I'd really do differently. Good structure, no overly imperative code, appropriate use of pipes (including not piping for calling a single function with a single argument, which many people do, but I think reduces readability), pattern matching, even Active Patterns. Nice use of a type provider with a web data source too.

Two very minor things:


You don't need new when calling a constructor; the compiler only recommends it when creating an instance implementing IDisposable. (I'm very happy about not needing new, because I find it terribly annoying and redundant in C#.)
I've recently started either putting if-then-else on a single line if short enough, or giving the then part its own line as well because that better represents the structure of the construct.