Much has been written about the production problems behind zombie blockbuster World War Z, including major reshoots and the scrapping of a 12-minute Russian battle scene that must have cost millions.

Then there are fans of the source novel, by Max Brooks, lamenting its radical adaptation.

It just goes to show that the only thing that counts is what's on the screen before you. For this is a cracking piece of entertainment, an edge-of-your-seat, spectacular horror-cum-action movie that doesn't relinquish its grip for a minute. A little like its monstrous hordes, World War Z really doesn't mess about.

We're used to zombie movies focusing on the small scale, with a group of protagonists holed up in a cabin or shopping mall, carnivores banging at the door. As his title suggests, Brooks's vision was a tad bigger than that. The film opens with a brief, no-nonsense prelude via television screens of brewing global catastrophe – an outbreak of rabies here, panic and social breakdown there. The world is so accustomed to tension, that it's entirely off-guard as a pandemic takes hold.

In the Philadelphia home of Gerry Lane (Brad Pitt), his wife Karin (Mireille Enos) and their two daughters, the mood is relaxed. What's martial law, one of the girls asks dad as she watches TV. "House rules for everyone." A UN investigator who's left his job to spend time with his family, Gerry is determined not to have a care in the world.

Breakfast over, they drive into town and an unfeasibly heavy traffic jam. The film is barely five minutes old; this is usually the time for character development and other preliminaries. Not here. Suddenly, all hell breaks loose.

The overrunning of Philadelphia by zombies is the first of three stunning sequences (Jerusalem and a passenger plane providing the others), with Glasgow's Merchant City and George Square standing in handsomely, heroically for the American city. The crowds are totally unprepared for the swarm of fast-moving human monsters attacking them – a far remove from the lumbering boneheads we know and love – which grows as each victim transforms within seconds.

The Lanes' escape is aided by the government, which whisks them away to an aircraft carrier. From here, Gerry – a war-zone specialist – is despatched to find the source of the plague, and hopefully a cure.

Whereas Brooks's book had multiple perspectives, the film chooses just one. Rather than narrow the global reach of the story, this approach actually intensifies it, as we experience Gerry's exhausting journey in search of answers: to North Korea, which provides a blackly comic vignette, with one gruesome yet practical way to avoid infection; Jerusalem, where Israel's usual skill for self-preservation through containment backfires; and to a laboratory in Wales, where the film switches to that more familiar zombie scenario – a handful of survivors, a room with answers, a corridor full of zombies blocking the way.

Alongside the atypical zombies is an atypical hero, Pitt's extremely engaging performance putting more textbook action heroes in the shade; how smart to play Gerry as a family guy, without strut or ego, who just happens to be extremely capable.

In keeping with the speed that the pandemic sweeps the globe, director Marc Forster drives the action along at an exhilarating pace. What his film lacks in cohesive plot is more than made up for by efficiency – it is thrilling, tense, occasionally scary, visually extraordinary. His ending may be much more low-key than a Russian battlefield, but it works, because like much of the film it's the very last thing we'd expect.