Henning Mankell was important as a crime writer because his Wallander books sparked what had become an explosion of Scandinavian crime fiction which went nuclear after The Girl With The Dragon Tattoo, and I find it hard to believe that Steig Larsson wasn't inspired in some way by The Fifth Woman one of the best of the Wallander series.
Otherwise, Mankell's influence was more in terms of marketing than style, though you can see a good bit of him in the best of the Nordic writers, Iceland's Arnaldur Indridason. But Mankell himself was influenced by the godfathers of modern Scandinavian crime fiction, Maj Sjowall and Per Wahloo and their ten Martin Beck books. Like Beck, Wallander is a dour detective with a depressing private life, and functions within an ensemble cast that both complements and contrasts with him. Mankell spends more time on Wallander himself, perhaps, which reflects the changing times to some extent (our literary cult of fictional personality) but also reflects Sjowall and Wahloo's own influences, especially Ed McBain's 87th Precinct.
Mankell was often dismissive of the label 'crime writer', but he was very generous to Sjowall and Wahloo, and wrote the introduction to the Harper Perennial reissue of the first Beck novel, Roseanna. When I wrote the introduction to Murder At The Savoy in the same series, I noted that its basic premise, the death of an industrial with fingers in many shady multi-national deals, is mirrored in Mankell's The Man Who Smiled (a very Martin Beck sort of title), and noted a few other parallels in the series. I also quoted the description of Beck's colleague Fredrik Melander, logical, calm, dull, with a 'modest' sense of humour, an excellent memory, and a propensity for being in the toiler whenever he was needed. As Sjowall and Wahloo wrote: 'briefly, he was a first-class policeman'. The one time I interviewed Mankell, appropriately enough at the Savoy (but in London, not Malmo) I asked if Wallander were in some ways an hommage to Melander. 'Oh, did they write that?' he replied. He also had little false modesty; I asked him who the man was who had greeted him just before we sat down. 'Oh, he's Sweden's second greatest novelist,' he said.
What also links Mankell to Sjowall and Wahloo was their dissection of the failures of Sweden's experiment in Social Democracy from a perspective often noted to be left-wing, but more accurately described as true to the ideals of that experiment. Mankell's political commitment is strong throughout his work, both in Sweden and Mozambique, and strongly consistent to a sense of rational help for those who need help and justice, and a society based on those principles. It was no surprise he chose to sail on the flotilla of ships trying to bring humanitarian aid to Gaza, it was even less of a surprise that he reported the summary murder of 10 activists by masked Israeli commandos, and refuted very simply and strongly allegations that the killings were self-defense. He had a field day with the fact that he was captured in international waters, brought to Israel, and then charged by the Orwellian government with entering the country illegally.
Wallander was well-served by television. Rolf Lassgard nailed his character, but Krister Henriksson was justifiably more popular, because he brought some humour to Wallender, just through his quick smile and twinkle in his eye; it made his interactions with the rest of the ensemble less confrontational. Kenneth Branagh's Wallander virtually eliminated the ensemble, concentrating on the superficial problems of Wallander's life, most notably drinking and shaving. It's good that the series has not been continued, like the Beck which for all its strengths has little of Sjowall and Wahloo left to recommend it. And it should be noted that Henriksson's performance in the final Wallander story, The Troubled Man, is every bit as touching as Mankell's own conclusion to the series (and it's one of the most overtly political of the series as well).
There isn't much humour in the books; Mankell wrote a comic novel, Tea Bag, about literary types and immigration—the humane portion about the life of immigrants in Sweden works muich better than the literary comedy. But his work for children is surprisingly good, including Chronicler Of The Winds, an adult story based on a play written to be performed in Portugese, in his adopted Maputo.
Faceless Killers, the first Wallander book, is a good place to start. One Step Behind and Fifth Woman are my idea of the series' best. I'd also recommend his 2006 novel Depths, (you can read my review of that book here), set on bleak islands in the archipelago during World War I; it is to my mind the most Bergmanesque bit of Swedish writing I've encountered and deeply moving. Of course Mankell was married to Eva Bergman, Ingmar's daughter, which may or may not mean anything.
We discuss Mankell in the second episode of The Crime Vault Live; I could not do the same on BBC Front Row that night because we were recording CVL at the same time. I might have said that sometime in the future people will look at Mankell as a transitory figure, between the trail-blazing of Sjowall and Wahloo and the worldwide phenomenon of Steig Larsson. But he's more important than that, and the consistency of his vision for both his iconic character, his other work, and beyond fiction to his country and the world, should make him a major figure no matter from what distance literary critics are looking back.