It's a heck of an achievement to make so much wilful offensiveness so very tedious. Postal III is doing, essentially, what Postal games have always done - a third-person shooter detailing the misanthropic adventures of the self-satisfied, amoral Postal Dude as he causes consequence-free carnage in small-town America. It's a scattergun salvo of obnoxiousness, but its purpose is not to be the bane of decency so much as it is to seek belly laughs from shock and absurdity. In Postal's book, that means porn, racial stereotyping, animal cruelty, a mile-wide misogynist streak and constant self-reference.
The theory, presumably, is that if everything and everyone is insulted, there's no real victim and thus no real prejudice. That's probably true, but there's very much a victim: the innocent purchaser of this desperately unfunny, low-tech mess of paper-thin sixth form humour. While something like South Park can back up its giggling nastiness with astute satire and a sense that its finger is on the world's erratic pulse, Postal III makes do with tired puerility and meatless toilet-grade humour.
Occasionally, it breaks the fourth wall, its slacker hero commenting on hoped-for controversies, other games, even the graphics engine it's using (an apparently outdated version of Valve's Source), and there are a few gentle chuckles to be had here - it's laughing at itself rather than celebrating itself, and it seems to have some sort of focus beyond desperate 'look at me! look at me! I'm so amazingly offensive!'
But none of the humour, good or worthless, can mask how lousy Postal III is as a game. As a shooter, it has terrible handling and inconsistent damage. As the GTA-gone-mad open urban world game it occasionally pretends to be, it's tiny, restrictive and low on variety and interaction. You may persevere hoping it'll suddenly find purpose and structure, but it ritually boils down to fending off hordes of cloned enemies (e.g. militant conservative anti-porn protestors, fast food joint workers in rice hats, angry hobos), usually while trying to protect something or someone else from harm.
What, in mere description, sounds like it could amusingly outrageous - for instance, attacking Sarah Palin lookalikes by throwing, uh, discarded tissue papers collected from the floor of a sex shop - is in practice a relentless, samey battle against infinite waves of foes with basic, boring combat. It offers some moral choices, which will alter the outcome of the game, but don't save it from its own inherent tiresomeness. If you want madcap, anything-is-a-target ultra-violence, Saints Row: The Third does much more, much better.
Occasionally it'll have a whine about Uwe Boll, who made a characteristically bad film based on the Postal license, or let you take a pop at Osama Bin Laden. Occasionally it'll feature cats, because the cat-based gun silencer is what people most remember about Postal II. Occasionally it'll feature scantily-clad ladies and Z-list celebrities. What it never actually is out outrageous, because its humour is now tired rather than scandalous. Since Postal II, an awful lot of pop culture and gaming culture entirely deserving of cruel mockery has arisen, but Postal III seems stranded ten years in the past - it's the boring middle-aged guy in the pub who tries to join in with your conversation, convinced he's being edgy but really he's just trotting out the same tired old lines.