The Plank with all the stars' signatures was sold at an auction in Colchester on 5 December 2011 for £1,050. It had been previously won by a family in Clacton for being the 100,000th visitors at an Ideal Homes Exhibition.
The Policeman is constantly taking off a striped armband and then putting it back on again. This is a Duty Armband, used to show whether the officer was officially On Duty or Off Duty. It was used from the early days of policing, when officers were expected to wear their uniforms at all times (e.g. travelling to or from work). Jimmy Edwards' character is trying to get home after his shift, so he's Off Duty, but plank-related incidents keep forcing him to go back On Duty. The use of Duty Armbands was discontinued not long after this version of The Plank was made.
Tommy Cooper replaced Peter Sellers who was forced to withdraw after shooting conflicts with another movie.
The actual plank carried by the two leads is still in existence and was signed by the cast. As another poster has mentioned, It was used as a promotional prize during the film's release. However the plank used during filming was some 10 ft or 12ft long but for reasons of practicality was cut down to about 4 ft by the time it was given away as the prize.