But don't take this the wrong way and assume that late payments are OK, especially on a regular basis!
If you've got 10 different credit cards with 10 different due dates, even if you check you balance twice a month, you're still bound to run into occasional problems with late fees or overdrafts. The Margin for Error is simply too high with this activity. In fact, the average credit card user probably gets charged more fees and interest than what is made back in rewards, otherwise this practice of extending credit card rewards would not be a sustainable business practice!
In my use of credit cards since 1999, I've probably averaged about 1 mishap a year, usually a late payment or an overdraft. But earning rewards and rarely carrying a balance has definitely paid off in providing me a net monetary gain in this endeavor. Let's use an example here: suppose Joe Schmo charges $1500 a month and pays off the balance entirely, except that he makes a late payment every 6 months. The average amount he's charged, including the late fee, overdraft, and/or interest is $40 each time. He averages 2% in credit card rewards each time (some of his cards only offer 1%, others offer bonus rewards on selected categories). So he gains $30 in rewards each month on average. His net gain from his use of credit cards each year is: 12*30 - 2*40 = $280.
If you occasionally carry a balance, make late payments, or incur overdraft fees, do take note and try to stop it from happening in the future but don't beat yourself up and lose sleep over those. It's not likely gonna have a noticeable effect on your credit score and the rewards you earn will likely cancel out the fees. If it becomes a regular occurrence (say multiple times a month or several months in a row), then it's probably best to take a time out from collecting rewards. Pay off all your balances and stick with 1 card (or use cash entirely) at least until you're confident you can pull finances back in order again.