Not at all! Nonetheless is a legitimate word, meaning "just as importantly".
Irregardless is not a word. People say it when they mean "regardless", or "without regarding the thing just said".
My mother used to use "irregardless", and I never gave it a second thought when I was young. Then one day, probably around middle school, I had that "wait a minute...

" moment.
"I could care less" always bothered me more, personally. I always want to tell those people, "okay, go ahead... care less!"

They mean, "I couldn't care less".