Why do people focus so much on APR when DPR should be the real killer?

I am new to credit cards (don't have one myself) but I am trying to learn a little more on them. I see that many people focus a lot on annual rates to calculate their payments, but if you don't plan to be a revolver and pay off your payments on time, as soon as possible, shouldn't you really be considering DPR instead of APR? I think read this in an old book once, but is it true that some credit cards are sleazy enough to charge interest rates on previous balances although you've already paid for them? How can this be possible, or am I confused?