I've owned a '70 Cougar, and two '67 Mustangs. All have had this problem:

1. Lock the door with the key. Unlock the door with the key. No problem.

2. Push the button on the door handle when the door is locked. Then try to unlock the door. It won't unlock. I have to go in through the other side and "play" with the lock. I have to repeatedly wiggle it up & down until it finally comes all the way up and unlocks the door.

3. Most people (a) get out of the car, (b) push down the lock, (c) push the button while shutting the door. This causes the same problem as #2. Basically, if the door is locked, I can't push the button. If I do, I can't unlock the door.

On my '67 coupe, I pulled the panel off the door and played around with the rods and sprayed WD-40 on a couple things. That pretty much eliminated the issue on that car. But I'd like to know if there's a specific part that's causing this issue.