I love Emergency!, it's one of very few shows I have on DVD. About the only "realism" complaint I have with it is that Dr. Brackett and Dr. Early (sometimes with help from Dr. Morton) do everything, not just in the ER but various surgeries later on.
That was also one of the few deviations from reality on Dragnet: one week, Friday worked homocide, the next week vice and drugs, the week after that juvenile investigations, etc. Of course, that was necessitated by the fact that, otherwise, Friday would be handling only one particular type of case for the entire series.
If they had spaced it out more, that might have been very realistic. I've heard of some departments rotating their detectives through different departments.