Among the arrangements done to make sure that the Torem will not steal from Terumat ha'Lishkah (or others will not think he did) why didn't the Mishna count the simple arrangement to have Beit Din look at him from outside or even come inside with him to make sure of it? Actually there were windows (or such) in the same place where Bet Raban Gamliel put their shekalim near the Torem or inside the Kupot.
Good question. In fact, RABEINU SHLOMO SIRILIYO says that they did exactly as you ask. They used to watch the Torem by peering into windows in the Lishkah. This is how he explains the phrase in the Gemara, "Mefaspasin Hayu b'Kalkalin."
According to the other Rishonim, we must say that the room was completely closed, with no windows or such (it makes sense that the money was kept in a closed vault). Although it obviously had a door, through which Beis Raban Gamliel would get their Shekalim into the Kupah, perhaps it was not proper to have people watching from the door, since they may start quarreling with the Torem to take from one side and not the other side in order to have their Shekel used for Korbanos, like Beis Raban Gamilier. (Only Beis Raban Gamliel, the family of the Nasi himself, was allowed this privelege, since it was obvious to all the the Nasi's house was derserving of honor.) Even Beis Raban Gamliel themselves probably did not watch the actual Terumah, but came immediately before it.
Be well, Mordecai