My house (Seattle area) has a Johnson Tee for the dishwasher. Turns out the air vent was never installed properly (20 years now) but it has worked fine so far. I'm curious if I'm supposed to loop the dishwasher drain hose up high on the back of the unit before attaching it to the Johnson Tee. I'm creating two traps that way. Could that cause me trouble with the dishwasher or drain?

if I'm supposed to loop the dishwasher drain hose up high on the back of the unit before attaching it to the Johnson Tee. I'm creating two traps that way. Could that cause me trouble with the dishwasher or drain? No! I gon't see much difference between a Johnson Tee,(see image} and a high loop. (see image) They both loop up tp form a air gap.
Your set up will cause bno problems for either the DW or the drain.

it has worked fine so far. I'm a great believer in, " If it ain't broke, don't fix it." If it's been working for 20 years then leave it alone.
We install high loops in my area. Good luck, Tom

You have Air Gap because Code calls for it. Otherwise, it would be plumbed as Tom shows you.

No loops with Air Gap. Go continuously upward with the 5/8" hose and connect to Air Gap's smaller inlet. No loops, no kinks, straight run. From Air Gap, connect with 7/8" hose to your Garbage Disposer or Branch Tee (whichever you have). Again, avoid loops and make sure you have no kinks. Otherwise, Air Gap will overflow.

Does the hose loop down and then back up before it connects to the Johnson Tee? Let me know, Tom