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1.
Depending on the situation punintentional means either an intentional pun as in pun intentional or as in an unintentional pun as in a pun on the word unintentional.
1. "Chop chop I need to get going" said the client in a whimsical way. "That was punintentional" laughed the barber.

2. "Did you hear about the fire at the campsite... it was so intense ( in tents)" said man 1. "Well that was a bad pun" said man 2. "Sorry it was punintentional" said man 1 with an aura of jokiness.
by The Man with the Golden Puns March 29, 2011
 
2.
When you slip up, in speech or text, and add or remove some letters from a word that results in a pun. This should be an unintentional slip-up, hence the term.
1. "Off to get some lunch. I'll be back in a bite. Whoa. That was punintentional"

2. "I punintentionally told her I'd meat her at my place."
by Rev. Mitcz August 07, 2006