Sweden thought they had the murderer when Christer Pettersson was convicted of the murder. He was permanently affected by a head injury he suffered as a young man and was prone to violence. Described as a petty criminal, drug user and alcoholic in Wikipedia he was identified by Lisbet Palme at a lineup. His appeal was allowed because the murder weapon could not be found, he had no clear motive and the lineup was flawed. Later he may have confessed. There are allegations, probably weak, that he mistakenly killed the Prime Minister thinking he was a rival drug dealer.
Victor Gunnarsson, a Swedish right wing extremist, was initially arrested for the murder but released as eyewitness evidence of his presence in the area of the murder was frail. He was killed in America by the ex-fiance of a woman with whom he was involved. As often happens with the deceased several acquaintances claimed he had confessed.
One of the more unusual groups identified was the Kurdish PKK, the Kurdistan Workers’ Party. Some members of the Party living in Sweden had conflict with the Swedish government. Probably the greatest reasons to doubt them were the efforts of the Turkish government to tie the PKK to the murder.
More plausible are the allegations against the apartheid government of South Africa who allegedly murdered Palme, an outspoken opponent of apartheid, because the Swedish government was secretly providing money to the African National Congress. Three different men were named by separate accusers as the killer of Palme. I doubt the South African government would risk the international complications of killing Sweden’s leader for the uncertain prospect of ending the payments to the ANC. Even if Palme were dead the payments could continue to be made.
More outlandish is the claim that the murder was instigated because Palme had received information that the Swedish armaments company, Bofors, had concluded a shady arms deal with India. The motive is questionable as killing the Prime Minister was unlikely to cover up the deal and there was a subsequent scandal.
Another author, Anders Leopold, claims a Chilean fascist, Roberto Thieme, killed Palme because he had given asylum to numerous Chilean leftists after the coup against Salvador Allende. The motive makes little sense to me as there were Chileans given asylum across the Western nations. One of them ended up in Melfort. I know another in Saskatoon.
The German weekly, Die Zeit, claimed Palme was murdered by right wing Swedish police officers. I very much doubt that a conspiracy within the Swedish police could have been maintained in secrecy after the assassination.
John Ausonius, a racist stock broker turned bank robber, was a suspect until it was established he was in jail on the night of the murder.
Solely on the basis of motive I doubt the conspiracy theories. Crime fiction fans certainly recognize the allure of conspiracies. They are far more interesting the lone killer acting for personal motives.
Conspiracy aficionados cannot accept that President Kennedy was killed by Lee Harvey Oswald acting alone. I became convinced it was Oswald when I visited the Museum in the Book Depository building and saw the distance and angle Oswald would have had to shoot Kennedy. It was easy shooting. Oswald, trained in the American army, would have found the shots straightforward.
As with Kennedy I think there is an important issue related to how the killing of Palme was done. One of the more unusual aspects of the Palme murder is that the weapon was a .357 Magnum revolver with a 4” barrel. It is a large handgun. It is distinctive and loud. I cannot see a hired killer using a .357 Magnum.
Swedish police diligently searched for 10 stolen .357 magnum revolvers. In Widipedia it states:
Out of these all have been located except the Sucksdorff revolver, a weapon stolen from the Stockholm home of Swedish filmmaker Arne Sucksdorff in 1977. The person who stole the weapon was a friend of drug dealer Sigvard "Sigge" Cedergren, who claimed on his deathbed that he had lent a gun of the same type to Christer Pettersson two months prior to the assassination.
While the lineup involving Pettersson was conducted improperly there is the visual identification by Palme’s widow who was slightly wounded in the attack.
I think, as with most assassinations, it was a lone troubled killer, Christer Pettersson, who killed Palme.