[High Praise! to Mental Floss]
19 Things to Look for the Next Time You Watch Die Hard
[Think you have a link that’s IMAO-worthy? Send it to harvolson@gmail.com. If I use your link, you will receive High Praise! (assuming you remember to put your name in the email)]

I never thought of that as a plot hole, I figured it was a case of ‘trust but verify’. Or rather, don’t trust until you verify.
When Hans finds the first dead terrorist in the elevator, he steps on to the elevator. John is on the top, and we see a view down into the elevator. I always figured that was how John knew “Bill Clay” was Hans.