The band is properly summonsed to magistrates' court for a traffic infraction, but they are then shown appearing before a judge in full robes. Magistrates are not Judges, and do not wear robes. Judges do not preside in UK magistrates' courts.
Heinz Burt is shown having eggs thrown at him, when in fact it was baked beans. (A wordplay on his name, Heinz)
At the start of the film where Geoff Goddard first enters the Shenton's shop, the film is reversed. The shop name on the glass and the "Open/Closed" sign are back to front, and the lock, handle and bell are on opposite sides compared with the shot that follows. The first shot of Geoff Goddard entering the shop is shown in a round mirror. The frame can clearly be seen with the shop background behind it.
The film is quite clearly set in 1963 but the registration plate of the black van in which the group are touring shows the suffix "D" which was issued in the year 1966.
The film shows Heinz Burt featuring in the TV show Oh Boy! (1958), which was shown on British TV some years earlier.
The legend reads 1965 when Mitch Mitchell is threatened with a gun while playing 'Night Of The Vampire' This song was recorded and released by the Moontrekkers in 1961 even predating Telstar.
Throughout this movie, people say "bands". Throughout the 60's in London, everyone said "groups". The word "band" only came into use in about 1970.
Telstar was not the first communications satellite. The Soviets already had one in orbit by the time it was launched, and the Americans had launched others. It was however the first one to be used commercially.