It made sense until you said...
The instances you mentioned, including late payments etc, don't effect the apr at all. Rather, they will alter the balance the apr is applied to and that's how you will end up paying more. As Steve said, the schedule of charges will have been clearly set out in the loan agreement so there's nothing to be challenging unless you're paying charges that weren't set out.
People should be facing up to debt not trying to get round it ... somebody has to foot the bill somewhere along the line.