The cops who come to capture and kill Zaphod are pure comic relief. This is especially clear if we look at the radio scripts, where these two get the totally ridiculous names of "Shooty and Bang Bang."
What makes the cops especially funny—or, depending on your mood, sad—is how they describe their feelings but then also describe how those feelings don't affect their actions: "I don't go around gratuitously shooting people and then bragging about it afterwards in seedy space-rangers bars, like some cops I could mention! I go around shooting people gratuitously and then I agonize about it afterwards for hours to my girlfriend!" (32.40). So: I don't want to do X, but I will because that's my job. Sound familiar? That's pretty much how all the bureaucracy in this book works.
Luckily for our heroes, the cops die because (a) they are aliens from Blagulon Kappa, so they breathe methane (33.32); and (b) Marvin makes their ship commit suicide by talking to it about how depressed he is. So sadness beats bureaucracy and politics, which is a very weird lesson to take. Does this book just want us to go and mope around the DMV or at insurance offices? Because we will do that if it works.