Don't say "sorry I'm late." Say "thank you for waiting." Don't apologize for giving the waitress a confusing order. Thank her for handling a challenging order. Even if you make a mistake at work, "thank you for double checking my work" can replace "oh, I'm so sorry for screwing up."
"Sorry" sends the message to others, and more importantly to YOURSELF that you aren't worth the inconvenience you've caused. Show your appreciation without putting yourself down by saying "thank you" instead.