What I've noticed in these shows are the basic murder/mystery plot. The first few minutes are used to introduce the characters who will be involved, aside from the 4 main characters. Dillon's side-kick, Chester, is played by Dennis Weaver. Anyway, the show opens up with the extras, and this is where you'll learn any motives which would make them look guilty for the murder that eventually takes place.
Although this is a western, the set up is like any murder-mystery. As in any murder-mystery, we, the viewer, can only know as much as our main characters. Matt Dillon, the sheriff of Dodge City, Kansas, must use the leads he has in order to find the killer. Often times, he has to track the person down out in the Kansas wilderness. Being a U.S. Marshall gives him this ability. Usually this person he is tracking is not the killer of the original murder in the beginning. But sometimes they have done something that will put them in jail, and often times they've killed someone along the way. Thus, you have a double-plot line, which is good for keeping everyone guessing. Misdirection is a basic key for a murder mystery. And depending upon how long a story goes, you could put in all kinds of red herrings and plot twists in to keep it interesting. Because “Marshall Dillon” was only 30 minutes long, it's easy to follow the plot line and see precisely how it is written.
What I've noticed is this is your basic plot all laid out. You have a mystery to solve. Doesn't matter if it is a murder. The mystery is what is important, and how it is solved.
You can learn quite a bit on how to set this sort of plot up by watching several of these shows. The simplicity of them helps one glean an understanding as to how to set up a very simple mystery. I've always enjoyed watching “Murder She Wrote” for the same reason, but mostly because she was a writer. I used to love watching this show because Angela Lansbury starred as an amateur sleuth and I loved her character as the mystery writer Jessica Fletcher. The plots of “Murder She Wrote” were really well done, with plenty of twits and turns to keep you guessing.
Learning and understanding how a murder plot is done, you might want to watch either of these shows. Besides, being entertained, I think you might get a few ideas for a plot all your own.