Arrowsmith conducts a trial of his serum by giving it to half the potential plague victims and giving the other half nothing. Anyone who tried this in real life would provoke protests, if not riots. So these trials are conducted by giving half the people a placebo and not telling anyone which they are getting.
In the night scene outside the research building when Dr. Arrowsmith's wife catches up to him, the snow becomes very scant and then a whole clump of snow falls, which looks like a stage hand got behind on their snowfall duties and then panicked.
When Arrowsmith's first patient in Dakota calls and says his little girl is sick and to come right away, Arrowsmith says he will, and takes off without getting the address.