The shuttle is shown being taken to the pad less than three hours before launch. However, it takes at least three days to prepare the shuttle once it is in position and it is usually there a month beforehand.
During training, an announcement reports that the shuttle will be launched in "T-minus 2 hours 30 minutes". A few moments later, the announcement gives the time as "T-minus 2 hours 59 minutes". Countdown timers don't go up.
Mr. T and the team are apparently practising their moonwalk in regular Earth gravity; a completely pointless exercise without a way to simulate the moon's weaker gravity.
Mr. T and the team are taking part in a "moonwalk test". However, NASA hasn't been sending manned missions to the moon since 1972, 13 years before this episode was made, therefore eliminating the need for moonwalk training.
The name of this episode is misleading. There hasn't been a Cape Kennedy since 1973, 12 years before this episode was made. It is now known as the Kennedy Space Center, located at Cape Canaveral.