The easiest test for the HP 82401A is the following: connect an HPIL cable linking the input and output of the interface, in effect creating a single-device HPIL loop. Turn on the HP71 and execute "CONTROL ON". If the cable doesn't work or if for some reason the messages coming out of the output and into the input don't make it, the calculator will respond with a "LOOP BROKEN" error message. The "CONTROL ON" command performs, among other things, a continuity test of the loop. For it to succeed the HP 82401A must be functional.
For the card reader, I guess that nothing short of writing a file and then reading it back will suffice as a reliable test. The problem with HP71 and HP75 magnetic cards is that the pre-recorded clocking tracks fade with age, so even if the card reader is fine you are likely to run into problems with many cards.