In 1996, Sweeney was sued for criminal defamation in France by the Barclay brothers, owners of The Daily Telegraph, but the claimants lost their case. At the time, Sweeney worked for the rival newspaper The Observer, and had given an interview on BBC Radio Guernsey alleging that they had been involved in corruption. The claimaints justified their legal claim in the French courts on the basis that the broadcast could also be heard in a small coastal part of northern France, although this was widely considered forum shopping. Sweeney was ordered to pay €3,000 by the appeal court in Rennes, France.
After formally joining the BBC in 2001, Sweeney reported on mass graves in Robert Mugabe's Zimbabwe for the BBC in 2002. By then Mugabe had banned BBC reporters from the country, forcing Sweeney to hide in a car boot to travel to a meeting with the Leader of the Opposition.
Sweeney spent four years investigating the cases of Sally Clark, Angela Cannings and Donna Anthony, three women who had been falsely imprisoned for killing their children. Sweeney's investigation helped to clear their names, and led to Sir Roy Meadow, the expert witness whose testimony had proved decisive in their convictions, being temporarily struck off the General Medical Council's medical register. Sweeney received the Paul Foot Award in 2005 in recognition of his work.
"Scientology and Me", a Panorama investigation into Scientology written and presented by Sweeney, was aired on BBC One on Monday, 14 May 2007. Prior to its airing, video footage filmed by the Church of Scientology was released on YouTube and on DVD that showed Sweeney shouting at Scientology representative Tommy Davis during a visit to Citizens Commission on Human Rights's exhibition "Psychiatry: An Industry of Death". The clips were sections of a documentary the Church of Scientology's Freedom Magazine TV produced about the BBC Panorama programme.
Sweeney remarked that he lost his temper due to days of harassment by Davis and the Church, and a strong personal reaction to the psychiatry exhibition. He had been visited at his hotel by Davis, despite not having shared the address with the Church, and had been followed on several different occasions. Sweeney labelled the clips "attack videos" and others say they were produced to discredit him and the documentary.
The BBC in response aired its own full recording of the incident. Panorama's Editor Sandy Smith explained what happened and how the BBC dealt with the incident in a post on the BBC's Editor's Blog. An internal BBC investigation found that Sweeney's conduct at one point in the filming was clearly inappropriate, but also noted that Sweeney had apologised for his outburst and concluded that as a whole, filming of the documentary had been performed in a proper and fair manner. Later on that same year in the BBC Panorama year in review Sweeney said "..a new generation is making up its own mind, and for that I make no apology". Sweeney went into a similar outburst in January 2009 when being interviewed on Radio 4 about the Tom Cruise film Valkyrie—clearly referring to the episode two years previously, as a part of a rehearsed joke.
In a segment on BBC Radio 4's From Our Own Correspondent broadcast in March 2008, Sweeney paid tribute to the late Scientology critic Shawn Lonsdale, who had died, apparently from suicide, a few weeks before. Sweeney looked back at the life of Lonsdale, and his eventful interview for the Scientology and Me programme that had been filmed the previous spring.
A follow-up Panorama programme also hosted by Sweeney, which at an hour is twice the length of the original one, was aired on 28 September 2010. This documentary contained interviews with high-profile ex-scientologists Mike Rinder and Marty Rathbun. Rinder in particular explained the tactics used by the church during the making of the previous documentary, while Rathbun primarily discussed the allegations of David Miscavige assaulting other members of the church. Rinder had been involved in the Scientology organisation's stalking of Sweeney.
In an undercover visit to North Korea, Sweeney posed as an academic from the London School of Economics whilst travelling with a party of students from the university, also including Sweeney's wife and another BBC employee. The BBC was accused of putting students at risk and of compromising the future ability of the university to pursue studies in other countries with strict regimes.
The BBC Trust Editorial Standards Committee investigated the complaints against the programme makers, and found that "the BBC failed to ensure that all the young adults Panorama travelled with were sufficiently aware of any potential risks to enable them to give informed consent. This was a serious failing, and the BBC is right to apologise to the complainants." They also found that Sweeney's wife, who was the trip organiser and tour leader, had a conflict of interest which was compounded when she became employed by the BBC for the programme.
Subsequently, however, a public statement signed by six of the 10 LSE student participants on the trip said that "We feel that we have now been put in more risk than was originally the case, as a result of the LSE's decision to go public with their story". They also indicated that they had no objection to the broadcast of the BBC Panorama documentary and that they were satisfied with how the BBC handled the trip. It was also revealed that an agent for the North Korean government had emailed threats to the LSE, which ostensibly motivated the LSE to take action against the BBC publicly. An LSE spokesman denied this. The programme was watched by 5.06 million people making it the number 1 show in its time slot and the second most watched show of the night.
The programme formed the basis of a book, North Korea Undercover, published in November 2013.
Sweeney was the presenter of a controversial Panorama about the ex News of the World undercover reporter Mazher Mahmood called "Fake Sheikh: Exposed". The Attorney General, Jeremy Wright, wrote to the BBC asking them not to show it in case it prejudiced any future trial, and Mahmood unsuccessfully tried to get an injunction to stop Panorama broadcasting recent video of him with no disguise. The broadcast was twice delayed and was finally transmitted on 12 November 2014. Following the programme the Crown Prosecution Service announced that they would reinvestigate 25 cases where people were convicted on Mahmood's evidence.
Sweeney presented the documentary he researched and investigated, Trump: The Kremlin Candidate?, first broadcast for Panorama on BBC One on 16 January 2017, four days before the Inauguration of Donald Trump. Exploring ties links between Trump associates and Russian officials and Russian interference in the 2016 United States elections, the documentary was well received by The Guardian, Radio Times, The National, and the Times Union. The documentary was screened in Perugia, Italy on 6 April 2017 at the International Journalism Festival. Investigative journalists Sweeney and Andrei Soldatov of Russia were in attendance at the screening.
Sweeney has won several awards throughout his career, including:
It's not a question of us setting out to call Scientology a cult – it's just a question of us asking legitimate questions, and their organisation being unwilling to engage seriously with us. And when you go in as a journalist to try and deal with that, it's explosive.