Lord McConnell tweeted it was “very strange” that Police Scotland had not intervened to stop incidents such as cars being vandalised, windows broken and people being “attacked in shopping centres”.
He later told another Twitter user his main concern was “town centre, public meeting and household violence” and called on the Scottish Parliament’s justice committee to look at how police had handled the referendum.
But the Scottish Police Federation said any disorder had been confined to “a minority of mindless idiots.”
Brian Docherty, chairman of the SPF, said: “It was inevitable that the closer we came to the 18th of September passions would increase, but that does not justify the exaggerated rhetoric that is being deployed with increased frequency.
“Any neutral observer could be led to believe Scotland is on the verge of societal disintegration yet nothing could be further from the truth.”
Mr Docherty said it was “preposterous” to suggest that normally law-abiding citizens would turn to crime as a result of the independence vote.
“One of the many joys of this campaign has been how it has awakened political awareness across almost every single section of society,” he said. “The success enjoyed by the many should not be sullied by the actions of the few.
“If crime has been committed it will be investigated and dealt with appropriately but, quite simply, police officers have better things to do that officiate in spats on social media and respond to baseless speculation of the potential for disorder on and following polling day.”
Police Scotland has denied media reports that leave has been cancelled, saying instead that some officers have had “rest days” rescheduled.
However, some police officers are understood to be secretly concerned about disorder at polling stations due to a large turnout.
There was anger and protests when voters were turned away from polling stations during the 2010 General Election after a larger than expected turnout at towns and cities across the UK.
Assistant Chief Constable Bernard Higgins said: “Our priority is to ensure public safety and security and facilitate a peaceful democratic process. The referendum is a significant event which is expected to attract a high electoral turnout. Policing arrangements are well in hand and will be appropriate and proportionate. As we approach the final stage of the Scottish independence referendum campaign, the service has once again geared up to respond to a period of increased activity, where the profile of Scotland will feature nationally and internationally.
“Detailed plans have been developed to ensure that we can respond appropriately to any issues that may arise. Where individuals do have concerns or wish to report a crime, I would urge them to come forward and report it through our 101 number where it will be dealt with appropriately.”
The former First Minister said incidents of violence, vandalism and intimidation could have been prevented had the force made itself more visible.
Lord McConnell insisted he was not pointing the finger at any one group, but Better Together supporters have complained about stone-throwing, being called traitors and facing threats that their houses will be torched.
And some No voters are said to be too scared to show open support for fear of reprisals.
Lord McConnell said yesterday: “The level of shouting-down at public meetings, people’s cars and houses being threatened and aggression in town centres and public places was preventable.
“I’m shocked that there hasn’t been more of a conscious effort by Police Scotland.
“More presence at the weekends, at public meets and one or two symbolic arrests of people would have set the right tone early on.
“I’m not picking sides, the evidence of these incidents is too strong and more should have been done to stop it.
“I think they have been surprisingly absent and I think they need to tell us why.”
Lord McConnell also criticised the force on Twitter, writing: “There is something very strange about the absence of Police Scotland intervention to stop referendum related vandalism and intimidation.”
Still Game actor Greg Hemphill backed his claims, adding: “Most of it has been surreptitious, hasn’t it? The wrecking of a sign under cover of night.”
To which Lord McConnell responded: “Posters least important. Cars vandalised, windows broken, people attacked in shopping centres.”
He then claimed if England or Wales were to be experiencing a referendum that Police would be facing a public hearing over a failure to do their job.
“If this was England & Wales @Keith_VazMP would be calling @policescotland in for a public hearing. Over to you Christine Grahame MSP,” added McConnell.
Lord McConnell’s accusations come as tensions between campaigners reaches boiling point.
Labour leader Ed Miliband was forced to abandon a visit to an Edinburgh shopping centre after he was surrounded by Yes supporters who jostled him and branded him a ‘****ing liar’.
His minders were forced to step in to escort him to safety.
Hundreds of campaign boards and banners have been smashed up, covered with offensive graffiti or destroyed.
Cars with Yes or No stickers in their windows have been targeted by vandals, along with shops sprayed with referendum graffitti.
Colin McClean from East Kilbride said: “ I’m scared to put a NO sticker on the car incase it gets vandalised. Realistic chance of it.”
Whereas student James Todd said: “And I don’t put a yes on mine for same reason. Stop pretending its one sided.”
Homes with ‘No Thanks’ posters have been pelted with eggs and one householder in Edinburgh had ‘coward’ etched into his front door.
Farmers have received anonymous phone calls saying their livestock will be set loose unless they take down campaign boards.
Last week, a ‘Yes’ campaign shop in the Capital was vandalised with swastikas and slogans reading ‘no thanks’ and ‘Nazis’.
Yes signs in a garden in Kirriemuir, Angus were smashed and the incident was reported to police.
Meanwhile, signs backing the ‘No Thanks’ campaign appeared to have been targeted by vandals by the A92 between Dundee and Arbroath.
Police Scotland Assistant Chief Constable Bernard Higgins said: “The referendum is a significant event which is expected to attract a higher than normal turnout.
“Policing arrangements for the referendum are well in hand and will be appropriate and proportionate. Police Scotland’s priority is to ensure public safety and security.
“We will respond appropriately to any issues which arise. We will not offer comment on the numbers of officers or their specific operational deployment.”