A few people have commented that the sign on the TARDIS door says "PULL TO OPEN" and I think someone
in this episode (Idris, maybe?) points out that the Doctor opens the door incorrectly by pushing. But this interpretation is not correct!! ... and I do find the fact that the issue pops up in the episode itself confusing...
The sign saying "PULL TO OPEN" is on the small door that opens to the compartment that holds the "POLICE TELEPHONE" that is "FREE FOR USE OF PUBLIC". This instruction is not for the door to enter the TARDIS- it is for getting to the phone. Besides, this is a Police Box. Only a policeman should be trying to enter a genuine Police Box, and he wouldn't need any instructions on how to get inside what is essentially his office/locker/mini-lock-up!
Years ago I built a Police Box as a joke (a weekend job using cardboard, tape, and a lot of blue paint!) and I had to recreate the sign, so I may have those words clearer in my mind than a lot of other fans!
I loved the episode. I think the TARDIS may be the most intriguing vehicle in story-telling, and I enjoyed seeing the "soul" of the TARDIS given a tangible form that could interact more directly with the Doctor.