The newspaper gives the date as February 3rd 1969. At this time of year it unlikely to be sunny, let alone hot enough to cause sunstroke. Indeed, the actual February 3rd 1969 featured snow showers in much of the UK.
Father Unwin is seen reading the The Times newspaper, but in close ups it is the Universal News.
How can a Hymek have room for luggage? It's power units are too large to accomodate any extra space for baggage.
The engine used is a Hymek locomotive, but the insignia at Bufflers Halt states that the line is managed by the former Southern Railway. This is an error, as the Hymeks were only used on the former Great Western Railway.
The mini-computer is constantly referred to as the KX20 (because that's how it was in the script), but the machine itself is labelled XK20.