A thief who stole a 38kg dumb-bell from a gym was caught trying to sell it on Facebook.
He was among more than 100 people caught using the social networking website for criminal activity in Cambridgeshire over a year.
The website was marked by police investigators as the modus operandi of the 104 crimes which happened last year.
Paedophiles have been using the website to groom children and teenagers.
One breached his sex offender’s order by using the site, and a sexual assault in the county was also linked to Facebook.
Three others were “arranging or facilitating the commission of a child sex offence”.
Others led to violence, burglary, racial hatred, making indecent photographs of children, threats to kill, wounding, harassment and intimidation.
Documents released under freedom of information laws revealed details of a number of the crimes.
In the dumb-bell incident, the offender posted on the website he had stolen the weights 10 years before by wheeling it from the gym.
The report said: “He has now attempted to sell this item via Facebook for £10, admitting the offence to the witness who has inquired after seeing it for sale.”
Another man was arrested for actual bodily harm after an online spat on Facebook.
The man followed the victim and attacked her outside a public library striking her four times in the head and kicking her in the rear left calf, causing injury. He was arrested at the scene.
Officers have urged Facebook users to report any suspected criminal activity on the website.
A Cambridgeshire police spokesman said: “We use a range of tactics during investigations including monitoring the internet and social networking sites.
“We would encourage anyone who comes across what they believe to be criminal activity online to report it to police by calling 101.”
And suspected criminal activity is also trending on Twitter.
The micro-blogging website has been connected with thousands of offences in Cambridgeshire, as the News reported.
The number of offences involving malicious or suspicious comments being posted on the website rose from 2,043 incidents in 2010 to 2,275 last year.
:: Police get clues on Facebook
A police force has requested the personal details of 11 Facebook users in Cambridgeshire as part of criminal investigations.
Plans to give the Government more powers to snoop on internet users have been criticised by Cambridge campaigners.
Andrew Watson, of the city branch of NO2ID, raised concerns about legislation to increase surveillance of internet communication. It was also criticised by Cambridge MP Julian Huppert.
But after learning of the Cambridgeshire force action Dr Huppert said: “We have to strike a balance between the need to investigate serious crime and a person’s right to privacy.
“If there is specific reason to believe that people could help with a criminal investigation then some access is allowed.”
Cambridgeshire police said Facebook can be used as part of criminal investigations.
Mr Watson said a warrant ought to be made necessary for police to search a Facebook page.