At one point Bobby Denver refers to "braces". As an American he would use the term "suspenders".
John, Barnaby and Peter are watching Bobby's show at home on a colour TV. Colour TV was not available in the U.K in 1955.
The newspaper front page story exposing Bobby's trick for crying on cue is an extremely obvious manual cut-and-paste job. The uneven lines, changing paper shades and wrinkled surface make it clear that the individual articles were clipped from different papers and messily glued to a backing page. This is a candidate for Worst Prop Ever.