What does $51bn buy you in a Black Sea subtropical resort these days? A heap of trouble, if the preparations for the 2014 Winter Olympics in Sochi are anything to go by.

With 120 days to go until the opening ceremony, around half that sum is alleged to have disappeared in corrupt building contracts. At the same time, human rights concerns are mounting and global controversy caused by Russia's new laws forbidding "gay propaganda" refuses to go away.

And that's before you get to more prosaic concerns over whether there is going to be enough snow in a resort where temperatures reach 30C in the summer and remain a relatively mild 10C even in February.

Vladimir Putin this week launched the longest torch relay in Olympic history, a 40,000-mile route that will pass through all 83 regions of the vast country, from Kaliningrad in the west to Chukotka in the east.

At the earlier traditional flame-lighting ceremony in Olympia, Russia's deputy prime minister, Dmitry Kozak, spoke of the "difficult road" that organisers had travelled since the Games were awarded to Sochi following a dramatic last-ditch intervention from Putin in 2007.

Kozak clearly has a gift for understatement. While it has become traditional to list the myriad concerns facing Olympic organisers before an event then to hail it as a triumph afterwards, Sochi is setting a new bar.

Putin has long hoped that the twin "mega events" of the Winter Games in 2014 and the football World Cup in 2018 will showcase Russia's power and – just as was the case in various ways for the past three Olympic hosts in Beijing, Vancouver and London – boost its image in the eyes of the world.

So far, it has done little but justify the cynicism of those who characterise the Games as an offering to Mammon rather than embodying the lofty ideals that echoed around the walls of the Hilton Hotel in Buenos Aires when Thomas Bach was elected to succeed Jacques Rogge as the International Olympic Committee's president last month.

Like the IOC, the organising committee president, Dmitry Chernyshenko, has argued that it is unfair to conflate the money spent on infrastructure with the direct operational cost of the Games. But it is a line that is harder than ever to hold in an area that will struggle to make full use of all the upgrades when it reverts to being a luxury holiday resort after the Games. The initial $12bn (£7.5bn) cost has risen almost fivefold, with critics putting much of the inflation down to the corruption endemic in the Russian construction industry.

The opposition figures Leonid Martynyuk and Boris Nemtsov claimed in a May report that up to $30bn of the budget had gone missing in "kickbacks and embezzlement" to close associates of Putin, claiming the Games had turned into a "monstrous scam".

"An absence of fair competition, clan politics and the strictest censorship about anything related to the Olympic Games have led to a sharp increase in costs and a low quality of work," the report said.

An 18-mile road between Sochi, where events such as hockey, speed skating and figure skating will be held, and the mountain sports cluster of Krasnaya Polyana has become a symbol of the huge cost increases, spiralling to a reported $8.6bn. "You could have paved this road with five million tons of gold or caviar and the price would have been the same," Nemtsov said in an interview with the RBK television channel in July.

Visiting the site with one year to go until the Games in February, Putin sarcastically berated the official responsible and fired him shortly afterwards. "So a vice-president of the Olympic Committee is dragging down the entire construction? Well done! You are doing a good job," he said on camera to Akhmed Bilalov, who left the country for Germany shortly afterwards.

The transformation of Sochi and the ski runs in the nearby Caucasus mountains, plus the construction of the roads, hotels and utilities required, has required an influx of tens of thousands of construction workers, including 16,000 from outside Russia. A Human Rights Watch report accused firms contracted to build venues including the Central Olympic Stadium, the main Olympic village, and the main media centre of cheating workers out of wages and requiring them to work 12-hour shifts with few days off. The companies were also accused of confiscating passports and work permits, apparently to coerce employees to remain in exploitative jobs.

Then there are concerns over human rights and freedom of expression that extend to Russia as a whole but will be highlighted more than ever in the runup to the Games. Campaign groups claim that local activists and journalists who have criticised preparations for the Games have come under pressure to keep quiet. Stephen Fry, among others, has already called for a boycott of the Sochi Games over new laws that forbid "gay propaganda".

It is an issue that will run all the way to the opening ceremony and beyond. The IOC is walking a tightrope, declaring that it is happy with Russian government reassurance that the law will not affect athletes or spectators and that the Olympic Charter will be respected but adding that it has no business to interfere with national laws.

The extent to which the IOC is able to hold that line, the response of Russian police and security forces to any protests from campaign groups and the IOC's response to athletes that speak out on the matter or display solidarity with the lesbian, gay, bisexual and transgender community by wearing rainbow colours will determine whether it becomes an issue that ignites during the Games themselves.

Meanwhile, Amnesty International has already voiced concerns over Putin's recent crackdown on freedom of expression, best exemplified by the Pussy Riot case. This week, the human rights organisation complained that a protest timed to coincide with the start of the torch relay against the lack of freedom of expression allowed in Russia had, with an apparent lack of irony, been blocked by authorities in Moscow.

It emerged last week that Russian authorities planned to limit public demonstrations and access to neighbouring territories during the Games, while local investigative journalists revealed that intelligence services have made wide-ranging amendments to networks in the area to allow for all pervasive monitoring of internet and mobile phone traffic.

By the time the Olympic flame reaches Sochi on 7 February next year for the opening day of the Games, along with 5,500 athletes from 80 countries, the total cost is likely to have spiralled further and the questions surrounding the most expensive and extravagant Olympics in history multiplied.

The huge expense and political controversy surrounding the Sochi Games will represent a baptism of fire for Bach. Part of his campaign ticket was to argue that the Olympics should become cheaper to bid for and host. He also admitted that politics and sport could not be separated in the modern world, while trying to cling on to the principle that the IOC had no right to interfere in sovereign states.

Such have been the wider concerns facing the Games that there has been little external scrutiny of the usual operational issues. Chief among them, as in Vancouver four years ago, is whether there will be enough snow. Organisers began stockpiling snow in February this year and will employ 400 snow machines to ensure they are not embarrassed.

Meanwhile, there are also concerns about whether the remote location will have an effect on the atmosphere and spectator numbers, particularly for the Paralympic Games that follow – prompting the authorities to cap rail and air prices to the region.

There is little doubt that the Sochi Games will be a success. With a price tag north of $50bn and so much political and personal capital investment by Putin, he cannot afford for them not to be. At what cost beyond the financial investment, and whether they will also inflict lasting collateral damage on an Olympic movement that claims to be in the throes of preparing for a new era, remains to be seen.

Total estimated costs of recent Olympics (including Games-related infrastructure)

Beijing 2008 $43bn

Vancouver 2010 $8.9bn

London 2012 $13.9bn

Sochi 2014 $51bn