The phrase "No offense," is like saying, "Get ready! Im gonna offend your pants off, but since I'm giving you warning, you're not allowed to slap me in the face."
Also, when someone says "Just saying..." with those imaginary three periods hanging off into the silence, they are in no way politely offering their opinion, rather, they are subliminally telling you
"You're too stupid to see that my opinion is a billion light years ahead of your opinion, and the sonic forces of my brain power are probably being read by the aliens on mars. Just sayin..."
"Oh, and no offense."