From an old printer'saxiom. Back in the early days of printing presses, each line of text had to be set up one letter at a time. Since the letters in the press were reversed (so they'd print forward), the printmaker (or typographer) needed to be careful not to confuse one letter for the other.
Reminding someone to "watch his p's and q's" means to pay attention to the details.
This axiom, regardless of its origins, has been common in post-victorian Britain as an abbreviation of 'to mind your manners' or, more specifically, to say both 'please' (p's) and 'thankyou' (thank-Q).
Thus the phrase 'watch your p's and q's' has been in use to encourage people to speak politely, especially children, who remember such phrases better than just instructions.
Kid 1: You spill my pint?
Kid 2: feck off!
Mum: Oi, watch you're p's and q's!
Kid 2: Sorry. Feck off, please.
Shaortening for "Pints and Quarts", which were the two main measurements for drinks. Whereas now we use pints, half pints, shots etc, there used to be Pints and Quarts.
Whehn things got rowdy, as they tend to do in pubs, you'd normally hear something like "Mind your Pints and Quarts" and a warning or some such. this was shortened to "mind your P's and Q's"
