Sometimes when I make buttercream icing, a grease trail forms around the middle of the mixing bowl.  Does anyone know why this happens what I'm doing wrong.

Not sure what you mean.  I don't think Ihave ever had anything like that happen.  Could it be the brand of shortening you are using?  Or maybe yoiu are not mixing it long and slow for best creamyconsistency.

Maybe you don't scrape off butter/shortening from the sides of the bowl with spatula. 

Sounds like it's melting as you mix it. 

bakerlady might have something there.  Is your bowl hot (from washing it) when you start mixing?