When Matt and Festus catch up to Doc's buggy and try to get him not to go on to the outlaw's cabin, Doc takes off. Matt says to Festus that they'd better not chase after him or they'd be seen, and he says they should walk. But they get to the cabin at basically the same time that Doc does.
At the show's very beginning, the stagecoach agent is holding a modern clipboard which was invented and patented in 1908.
The repeated reference to Julie Blane's (Jean Arthur) long stagecoach ride makes little sense since she could have taken the railroad.
When Doc gets to the cabin with the food for the baby, there's a shadow on the outside of the fireplace chimney. All characters are accounted for, so it must be a member of the crew.
When Doc goes in the general store to get baby supplies he calls the store clerk Jonas. However that was a character played by Dabbs Greer. The clerk was played by Roy Barcroft, and his character is called 'Roy' and appeared many times in the Gunsmoke series. Even in the credits it has Roy listed for Barcoft's character..