It is Edgar Kennedy, one of the most frequently seen actors in the films of Laurel and Hardy. He often played a police officer, but no matter what type of character he was playing, his character was slow to fully anger, instead just getting more and more frustrated and annoyed until he can no longer contain himself. This became known as the "Slow Burn."
He appeared in nearly a dozen Laurel and Hardy films, and twice he was the duo's director. During his career he also appeared with Charlie Chaplin and the Marx Brothers.
Here is another photo of Kennedy as the put-upon police officer:
