As the senior staff are in the outer office of the Oval Office, CJ is wearing her glasses as she crosses the threshold to enter the Oval Office her Glasses disappear without her having moved to take them off and they are not in her hands.
While giving the President his exam, Captain Tolliver is wearing his Service Khaki uniform when Navy regulations require all personnel to wear their Service Dress uniforms in the White House.
Captain Tolliver reports that the President's blood pressure is 131/84. Manual blood pressures are always given in even numbers. The President's blood pressure would be given as 130/84 or 132/84.
While giving the President his exam, Captain Tolliver says that his temperature is 56 degrees. If the thermometer was measuring in degrees Celsius it is more likely it would be 36 degrees. At 56 degrees, Predident Bartlet would have been running a temperature of 132.6 degrees Fahrenheit, not humanly possible.
The aircraft carrier USS Coral Sea had already been decommissioned for nearly 10 years prior to the date of this episode. Also, F-14 Tomcats never operated from the USS Coral Sea during any of its deployments.
After Sam finds the call girl Laurie, she explains to him that she has broken some State laws, but claims to have never broken any federal laws. However in pilot she is shown in bed smoking marijuana which is a federal offense.