Watch when Doc pours water into the pan to heat the babies' bottles. It appears his kettle is leaking!
When Doc goes into Matt's office after the babies' mother dies, Milburn Stone calls James Arness by his real name instead of his character's name. Doc very plainly says "hey Jim" instead of "hey Matt".
Doc (to the crying triplets): You can do better than that - I've heard one coyote put up a bigger howl than that.
(Babies start screaming)
Doc: Now that's better - that's a lot better!
Judge: Competent people will come here and take those infants by force, if necessary!
Doc: Alright, let 'em come, judge, and whoever they are they'll get a decent burial!
Festus: And there's three of 'em too!
Festus: Miss Kitty, babies is about the most wonderfullest thing there is, but as far as bein' looksome, there ain't one of these that could pass without pushin'.
Kitty: Some people just have an unlimited capacity for love.