[BJungNan]

And one more opinion...

According to Webster's:
Alluding to the difficulty a child learning to write has in distinguishing between p and q - 1779

[pcottraux]

It's related to not getting your D's stuck in your Z's.

[Delta 21]

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[dfwgator]

"You just mind your Ps and Qs buster and remember who you're dealing with… "

"Bueller, Ferris Bueller."

[Jaysun]

In spite of what I told you in a previous post (quarts, pints) I think the most plausible explanation is the one involving typesetters.

[Echo Talon]

My dad used to say that to me all the time along with a swift smack upside the head. :)

[TN4Liberty]

I found this at http://www.wordorigins.org/wordorp.htm

Mind Your P's & Q's
The phrase dates to the late 18th century--at least 1779. The exact origin is unknown, but several competing hypotheses seem to be the most likely.

The first is that it derives from the phrase p and q which was an abbreviation for prime quality. This English dialectical term dates to the 17th century. So to mind your p's and q's would mean to be exacting in detail and ensure high quality.

The second is that it refers to difficulty children had in learning to distinguish between the letters p and q, being mirror images of one another. To learn one's p's and q's is a phrase meaning to learn one's letters is first recorded around 1830--somewhat later but not impossible as the origin. Often this explanation is identified with printers and distinguish between a p and a q in type, but the early use exclusively deals with children, not printing.

The third, first suggested by Farmer and Henley at the turn of the 20th century, is that the phrase comes from the practice of maintaining a tally in pubs and taverns. Marks under column P, for pint, or Q, for quart, would be made on a blackboard. To tell a bartender to mind his Ps and Qs would be to tell him to mind his own business and get back to work.

Another commonly suggested explanation is that it is a variation on mind your pleases and thank yous, a plea for gentility and manners. There is no evidence to support this, nor does the please and thank you phrase appear anywhere except in explanations of the Ps and Qs origin.

The last is from the world of printing. Typesetters had to be skilled in reading letters backward, as the blocks of type would have mirror images of the letters. The lower-case letters p and q were particularly difficult to distinguish because they are mirrors of one another and located in bins next to one another. Typesetters had to be particularly careful not to confuse the two.
Which is the correct one is anybody's guess (except the fourth which is certainly false). I favor the second explanation, but that is just a personal preference.