When the townspeople are helping Sheriff Matthew stand up to Zachary Brett, the Reverend and Hank are standing in the background. In the next shot, we see Hank and the Reverand walking around the corner of the clinic to come join the crowd.
Dr Mike stated that police don't carry guns in England. But even in 1884 they could be armed if they chose. In the 1930s, arms could be issued by a sergeant.
Dr Mike appears to be wearing frosted lipstick which was not invented until the 1920s.
Obviously the writers forgot about the fancy pistol Miss Olive gave to Matthew in season one.