Continuity mistake: As Alan makes his telecall to Grandma, the close-up of his hand dialing her number shows the push-button dial panel with letters on the left and numbers on the right, but on the puppet-sized telecall unit, the numbers are on the left and the letters are on the right.
Continuity mistake: When Alan contacts his father at Tracy Island, Jeff asks him "How's the situation, boy?" Alan informs him that Grandma has passed out in the heat and Alan's face is covered in sweat. But after a quick cut to Jeff saying "Passed out?" we return to Alan, and the sweat on his face has disappeared.
Continuity mistake: When we first see Virgil in the cockpit of Thunderbird 2 in the launch sequence at Tracy Island, he has nothing on his head. Later on, when we see both him and Brains, Virgil is now wearing his International Rescue hat, but when we see Virgil after the launch, the hat has gone.