The Twitter account @SochiProblems, with comments on issues ranging from supposed spray-painting of the grass to signs banning fishing in the toilets in Sochi, is vying for attention with official feeds from the Russian organisers.
The Internet is also full of jokes drawing on a wealth of material - reports of corruption around the Games, the Russian president's stance on gay rights and widely circulated photos from the Games facilities showing two toilets in one cubicle.
One post shows a drawing of five coloured toilet seats in the shape of the five interlocking rings of the Olympic Games symbol. In a play on words, it says Srochi 2014 underneath - which roughly translates as Crap 2014.
Three days after it was set up, @SochiProblems has 190,000 followers.
That is not good news for Putin as he tries to use the Games to enhance Russia's image and show the progress it has made since the end of the Soviet Union in 1991.
A cartoon on Facebook shows a worried Putin running with an Olympic torch which, instead of a flame, has a burning fuse as if it were a bomb.
One tweet declares: "Putin has personally guaranteed security for sexual minorities during the Olympic Games in Sochi." Attached is a cartoon of a ski jumper in mid-air with skis in the colours of the rainbow Gay Pride flag, surrounded by four security guards also in mid-air, pointing their rifles.
Despite Olympic chiefs' high praise for Russia's Games preparations, Moscow and Putin have attracted mostly negative publicity abroad on everything from unfinished Sochi hotels to reports that stray dogs are being poisoned in the host city.
Although he won a third term as president in an election in March 2012, Putin is a constant target on the Internet for Russians who are fed up with his 14-year domination of the country as president or prime minister.
Mocking the threat posed by Islamist militants who have warned of an attack on the Games, one photoshopped picture shows what looks like a group of bearded men in camouflage posing with the silver-and-red Olympic torches.
Putin has dismissed talk of widespread corruption around the Games. But a popular online joke plays on the accusations that some of the funding for the Games has been stolen or misspent, asking why a person refuses to watch the Olympics on TV.
The answer goes: "Imagine you get your salary and some dudes beat you up in a back street and take the money. Then they email you a video of the great time they had spending the money in a casino, on Blackjack and on prostitutes. Would you watch and root for them"
A cartoon of the athletes' Olympic village in Sochi shows a sign reading "Gay athletes' quarters" being nailed to a closet door - the implication being that they are expected to stay in the closet, or not go public with their sexual preferences.
The satire has touched a raw nerve among some Russians who, like Putin, believe national pride is at stake at the Games.
"Enough is enough. This is beyond the boundaries of decency. It's a sporting event and that's what it should remain, not another excuse to have a go at Russia," one Russian official complained, but asked not to be identified.
One website (www.paleofuture.gizmodo.com) has also hit back, saying it has exposed eight pictures that paint Sochi in a bad light which are either out of date or were not taken in the Black Sea resort at all.