The mediators were within jogging distance and they wear uniforms, how can you not spot them immediately and figure out that you're in a punishment zone? The Edo don't seem to have access to advanced especially advanced technology
Hmh? Advanced technology would appear very likely since our heroes considered themselves justified in contacting this planet in the first place. Also, the local God is clearly manifest in the lives of the natives - it is only "said to be up there" but known
to "make itself felt most fully". When Liator says the latter, he's rather blatantly speaking of the God's ability and willingness to deal with situations like the one at hand... So, God is quite likely to provide the Police Department with the monitoring and transportation services it needs.
being in a punishment zone and being caught is less likely than being caught in a system that punishes you no matter where the crime was committed.
Only if an offender can plead "being outside the zone". Which he of course can't do: if he gets caught, he was
inside a zone, or at least can't prove otherwise. The odds of getting punished are not reduced by the zone system in practice.
Why the zones exist even in theory (as opposed to the entire planet constantly being one giant zone) is probably to provide a modicum of plausibility: the criminals know there are very few enforcers, and this system caters for the fact.
Also, note that the system is not intended to combat specific crime. It is intended to terrorize the populace. Those who believe in it become exceptionally docile and cautious; those who don't become bold and visible and are quickly culled out of the gene pool by judicious executions. That is why the nature of the crime is of no relevance, and why the punishment for all offenses is death rather than, say, months-long torture.