I noticed when I first used the Skyforge in Whiterun that I was holding the wrong end of the metal when I went into the cutscene where I bang out the metal on the anvil. As a matter in fact I was already holding the metal piece in my hand as I was pulling on the cord to heat the forge before pulling the metal hot from the red hot end. Not game breaking and I probably would.not have noticed it if I wasn't watching the process.

Edit: This happens at every forge I go to.