In the shot that Dr. Mike and the Coopers are in the wagon that was used in the credits, on the close-up, Colleen is standing behind Mike. When the camera switches to a far shot Colleen is very visibly sitting. The camera switches to the close-up and she's standing again. This goes back and forth.
Dr Mike made no effort to swish water around in the quinine bottle to get the last dose of medicine out.
At the 10 min mark a 7 day mantle clock can be seen but it is not working. Its pendulum is stopped since the tick tock was likely too loud for the dialogue in the studio.
Grace is seen wearing lip gloss which was not invented until the 1930s.
The reflection of several multicolored studio lights are visible on the metal pistol Matthew takes out of a box.
When Dr. Quinn and the children discuss who are immigrants, the talk about Robert E. as if he came over on slave ship. It is more likely that Robert E. was born in the US as a slave.