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.
The series is very popular in Australia, even being the subject of a recurring parody ("Inspektor Herring") on a local sketch comedy show.
It's also quite popular in Russia - it gets regular reruns up to this day and inspired a semi-Foreign Remake called Mukhtar Comes Back - the dog's nickname was borrowed from an older Soviet movie, but the series overall are reminiscent of Rex.
Poland has its own version as well, Komisarz Alex ("Inspector Alex") and it gained a popularity among the viewers.
Harsher in Hindsight: "Finally The Monster is Dead" revolves around the murder of a respected business man who is discovered to have been sexually abusing his daughter for years. This show is made and set in Austria. Do the math.
Ho Yay: Alex Brandtner and Christian Böck. They start calling each other by their first names while Höllerlin still referred to him as "the new guy" or just "Brandtner". And then, in an early episode, Alex tenderly wiped blood from Christian's face. Not to mention that they always stand very close to each other.
Tear Jerker: Moser's death, in spades. The fact it comes right after the guy has settled with a girlfriend he's happy with is bad enough already ("happy people make for boring television" indeed), but the "Please Wake Up" scene at the end manages to make it even worse. Rex does the final "Please, Wake Up" with a squeaking animal's toy it is holding in its mouth, before it gives up and sadly leans its face on Moser's dead body. And then the screen fades to white. Damn.
Values Dissonance: For a show that on one level is tonally very much akin to a cute, kid-friendly "heroic animal" show like Skippy or Lassie, complete with delightfully corny humour and sometimes implausibly anthropomorphised behaviour by Rex, on the other hand the crimes they investigate are generally murders, and can be quite horrific in nature, not to mention occasionally featuring full frontal nudity.