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“Combat Rock” is the Clash’s most commercially successful album, and it’s also the one that tore them apart. Although it contains their two most-popular songs — “Should I Stay or Should I Go” and “Rock the Casbah”— and made them into one of the world’s biggest bands, it’s a disjointed, confusing album, with three absolutely killer tracks, a handful of middling ones and a bunch of indulgent solo experiments. And although a similar assessment could be made of this album’s predecessor, 1980’s sprawling triple-disc “Sandinista!,” time has been kinder to that set’s ambition. Still, even though this 40th anniversary edition of the Clash’s fifth full-length — which also includes a bonus disc of concurrent material  — shows that its flaws have not aged well, it’s still a document of one of rock’s greatest-ever bands going out in a blaze of glory, even if no one realized it at the time.

The album is disjoined for a reason. In 1982, the Clash were on the brink of a superstardom they’d probably never imagined, thanks to the masterful 1979 “London Calling” album and their explosive live shows. However, guitarist Mick Jones, the group’s musical mastermind, was increasingly at odds with co-founders Joe Strummer and Paul Simonon, ace drummer Topper Headon was succumbing to drug abuse, and all of them were falling prey to overwork and, ironically, the rock and roll excesses that punk rock had originally disdained, particularly fame and drugs.

By late 1981 they’d completed sprawling pile of songs that Jones sequenced into a 17-song, 77-minute album under the working title “Rat Patrol From Fort Bragg” (which remains officially unreleased but easy to find online). But the only person who liked that version of the album was Jones, and the group brought in veteran producer Glyn Johns (now world-famous thanks to his fashion-forward co-starring role in the Beatles’ “Get Back” film) to help bring it into sharper focus. Songs were retooled, some were dropped (with most of those appearing as B-sides or on the 2013 “Sound System” boxed set), and the band stumbled toward global stardom even as it was imploding. Headon’s drug abuse resulted in his firing shortly before the album’s release, and although the group barnstormed across the U.S. opening for the Who in the fall of 1982, Jones left the following year and the group plodded on with replacements for one dreadful album, “Cut the Crap,” before packing it in.

Yet even an uneven Clash album contains more greatness than most, and along with the two hit singles, the highlight of “Combat Rock” is the vividly atmospheric “Straight to Hell.” With a haunting vocal performance from Strummer and intricate percussion from Headon, it’s one of the group’s all-time greatest songs, and gained a second life when sampled by Diplo for M.I.A.’s 2007 hit “Paper Planes.” Elsewhere, “Know Your Rights” is a barking rant from Strummer, “Atom Tan” is a stab at the call-and-response vocals they’d used so successfully on “London Calling” — and even includes a brief, albeit off-color shout-out to Cheap Trick — and “Inoculated City” is the kind of Jones-led melodic song that he would perform with his post-Clash group, Big Audio Dynamite. (Ironically, Strummer and Jones would reunite to write most of the songs on that group’s 1986 second album, “No. 10 Upping St.”)

But the rest of it, quite honestly, is a mess. The painfully dated “Overpowered by Funk” sounds like a tepid attempt at Prince circa “Dirty Mind” and features a terrible rap from graffiti artist Futura 2000. Beat poet Allen Ginsberg plods desultorily along with Strummer over a lightweight funk rhythm on “Ghetto Defendant”; “Sean Flynn” is an aimless fusion of Asian influences and dub; “Car Jamming” is a tuneless rave-up. What “Combat Rock” is really missing is the feeling and chemistry of a band, musicians creating something greater than the sum of their parts, which is present in spades on nearly all of their preceding work — even the unfocused “Rat Patrol From Fort Bragg” feels more like a band effort. As a whole, “Combat Rock” is a travelogue of New York City nightclubs, American TV, Scorsese films and cocaine.

This anniversary edition appends an 11-song collection called “The People’s Hall” that gathers some stray tracks from 1981-82 like the stand-alone single “This Is Radio Clash” (the most hip-hop song they ever released), three tracks from “Rat Patrol” and other “Combat Rock”-era ephemera, most of it previously released on B-sides or compilations; released separately last month are two remixes of tracks from the album led by Ranking Roger, toaster and co-vocalist of the English Beat. There are no lost treasures but they do provide context for the album; the liner notes give scant information about the songs but do provide a detailed history of the West London house where some or all of them were recorded (which the band apparently shared with Motorhead), and from which the collection takes its name.

But for all of its indulgences, four decades on from that hot summer of 1982, “Combat Rock” remains a ragged final blast, the flawed swan song of one of rock’s greatest bands.