Women and girls would never have worn pants in public during this time period, especially in town.
Several times paper pads are shown being used. These were invented in 1888, and would not have been used during the time period of the show.
Lucas McCain's rifle is a modified 1892 .44-40 Winchester, even though the series clearly establishes itself in the 1880s.
The series takes place in the 1880s, with Lucas and Mark McCain moving to North Fork from Enid, OK; Oklahoma Territory wasn't opened up for official settlement until April 22, 1889, and Enid didn't come into existence as a town until the Land Run of 1893.
The majority of the men's shirts shown have buttons down the full front of the shirt. However, men's shirts were only manufactured in this style the first time during the early 1920s and didn't become popular until later 1920s/early 1930s.
The hair styles worn by most of the men and many of the women during the series reflect the 1950s/1960s filming of the program rather than its 1880s setting.
Lucas McCain sometimes cocks his rifle one-handed using the oversized cocking lever. But the way the rifle was modified for rapid fire, with a special screw that pushed the trigger, it would fire whenever it was cocked. So when he cocks it by spinning it around his hand, the rifle is actually empty of ammunition and not ready to fire.