Driving LED's with PWM

[Art]

Rapidly switching DC on & off (PWM) is a square wave. It's still DC.
If you vary the duty cycle from 50% it will look different, but we still call that a square wave.

You can measure the current with LEDs running constantly for a single row like it sounds like you're doing.
If it's a POV display where you cycle rows, then no more than one row (or column depending on how you look at it)
is going to be powered at one time, so you can assume the total of the switching transistor and LEDs for a
single row is the maximum current that your display will draw.

Be careful trying to measure PWM with a digital multimeter.
The digital multimeter is a microcontoller too, and can only take samples at a certain rate that is not synced with your PWM.

I believe the best insurance against software failure is your watchdog timer.
The best place to clear it is in your display routine that cycles the rows.
Depending on complexity, I suppose some insurance against hardware failure is also prudent.