External Interrupt Timing

If there is an interrupt attached to a pin looking for a falling edge, once the falling edge is detected, how many ops does it take to enter the callback function?

Some registers are pushed onto the stack. That is the main delay. You have to check the code that the Arduino generates.

If you use AVR code, I think it is possible to have a minimal ISR that pushes almost nothing to the stack.

Nick Gammon has some testing that shows a few microseconds. http://www.gammon.com.au/forum/?id=11488