When Danny and Baez opened the barrel revealing the victim's body that had been there for a long time, they both recoiled at the smell. However, the barrel would not have been airtight so the smell would have revealed its presence.
Those barrels are in fact air tight.
While in the doctor's office, when Danny punched the filing cabinet in anger, the drawer popped open showing that it was completely empty.
There are no telephone lines going into the phone on the Secretary of the Mayor's desk.