These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Angst? What Angst?: Played with in the pilot in regards to Brisco not seeming too broken up by his father's death. He reasons that with the old man a lifelong lawman, he had a very long time to prepare for him dying on the job. However, at the much later graveyard scene, Brisco is clearly in mourning and regrets not resolving their problematic relationship. Later episodes show that while he maintains his professionalism, Brisco doesn't take his father's death lightly and still misses him.
Awesome Music: Randy Edelman's theme music (as well as his score for the Pilot Movie) - surprisingly, and sadly, it appears the theme has been mostly Lost Forever, as the actual song is not available to purchase on Amazon (instead, just a bunch of particularly bad ripoff versions made using primarily a horn) and there are no easily-found videos on YouTube containing the theme.
Ensemble Darkhorse: Pete Hutter was meant to be killed in the pilot, but Boam and Cuse were so impressed with the actor that it became a recurring role, complete with Running Gag of surviving in very unlikely circumstances.
Dixie Cousins very much so. She was always intended to be a recurring character (unlike Pete), but as part of a Love Triangle with Brisco having to decide between her and Amanda Wickwire. However, the actress made such an impression in the Pilot Movie that the writers altered their plans to retain only Dixie as a Love Interest.
Professor Wickwire. A nice, quirky borderline-Mad Scientist, who - unlike his daughter - was retained from the pilot to be a recurring character. Helps that he's played by John Astin, too.
Sheriff Aaron Viva may qualify, as he originally made a one-off guest appearance only to then play a major role in the two-part finale.
"Funny Aneurysm" Moment: At the end of "High Treason, Part 2," there is talk of further adventures for Brisco and Lord Bowler, but Bowler stresses "after a hiatus" first. The episode was shot as a season finale (hence the hiatus joke), but the series was cancelled over the summer break.
He Really Can Act: Let's face it, Bruce Campbell is one of those actors who really needs to do nothing more than be himself to get the audience invested. But a few scenes in this show, like Brisco's visit to his father's grave at the end of the pilot, show that he really can be an effective dramatic actor when he wants.
Screwed by the Network: On the DVD, Carlton Cuse laments that had they been able to make it to a second season, the show probably could have lasted for a very long time. David Duchovny, star of another Fox show that debuted in 1993 (and which followed Brisco County on Friday nights), also lamented its fate.