Just as a matter of interest. Rather than me watching someone interview an artist. (Which is what I believe the sentence is meaning) What if myself and an artist were watching an interview. How would that change the sentence structure?
Hmmm. This one could stay actually, especially if for some reason you wanted it to be ambiguous. If you wanted to clarify, then I'd suggest:
Oglądam wywiad razem z artystą (I'm watching an interview together with an artist)
Razem z artystą oglądamy wywiad (Together with an artist we're watching an interview)
That's an interesting question you asked.
"I am watching an interwiew of an artist" is correct, isn't it? "With an artist" sounds like an artist is watching that interview with me... I am no English native speaker, though.
Apparently it's fine. Still, I think that "with" is the default version, even if it sounds a bit like you're watching it together.
Added "of", anyway.