DAMASCUS—Demonstrators across Syria pressed their demands for regime change Friday in what some observers called the country’s biggest protests here yet.

At least 24 people were killed Friday, human-rights monitors said. Violence continued as President Bashar al-Assad confronts not only mounting public anger but also a growing lawlessness across Syria—ranging from the vigilante groups and Assad supporters who have mounted deadly reprisals on protesters, to a wave of petty crime, uncollected garbage and unauthorized construction.

In three and a half months of Syrian protests, demonstrators have so far failed to reach their goal of ending Mr. Assad’s rule. But some observers say the examples of disorder unleashed by protesters’ actions—including the government’s use of non-state actors to quash dissent—is eroding the state authority that has been a cornerstone of the legitimacy of the Assad regime, which has long portrayed itself as a guarantor of calm in a country of mixed ethnicities and religions.

“The longer the protesters continue to defy the regime and its security forces, the more scope there will be for general lawlessness,” said a senior Western diplomat in Damascus. “This could undermine the regime which has consistently trumpeted its ability to provide stability.”

Daily antigovernment protests increased this week and Friday’s demonstrations on the day of prayer drew crowds that some activists estimated to number a half-million. Such numbers aren’t possible to verify, but diplomats also estimated the turnouts to have been among the country’s largest thus far. Huge protests were held in Hama and Deir Ezzor, and in areas of Damascus and other large Syrian cities.

On both Thursday and Friday—dubbed the “Friday of Departure”—protesters poured out in several areas of Syria’s second city, Aleppo, a commercial hub that has so far been relatively quiet. Activists, who say discontent with the regime is widespread there but that residents have been too scared to take to the streets, called for a called for a “volcano” of protesters there to jumpstart its uprising.

Videos posted on a central activist Facebook page showed protesters in Homs holding red cards calling for Mr. Assad to go and shouting, “the people want to topple the regime.” Residents and activists reported widespread tear gas and gunfire.

In Hama, where Syrian army and security forces pulled out two weeks ago, posters of Mr. Assad have been torn down and even traffic police are gone, residents say. The army continues to sweep villages in the northwestern province of Idleb, where actvists and rights groups say 10 people were killed Wednesday and detentions are continuing.

U.S. Secretary of State Hillary Clinton warned again Friday that the Syrian regime has limited time left to usher in reforms.

The Syrian government has attempted to regain support in recent days by inviting in some foreign journalists and allowing a group of opposition intellectuals to meet. Journalists have written that they are accompanied by minders and several attendees of the conference have said they were subsequently threatened. Most of Syria’s fragmented opposition has said they will refuse to attend a national dialogue on July 10, suggesting more violence may lay ahead.

At least 1,400 civilians, and more than 300 soldiers and security forces, have been killed in protests that started in mid-March, according to human-rights groups.

A significant constituency in Damascus and Aleppo have remained loyal to Mr. Assad—primarily for the social, economic and political stability his regime has brought.

But Damascus has seen an increase in petty crimes and scofflaws as government forces are busy elsewhere or reluctant to annoy the population, some Syrians believe. By day and at night, vendors with racks of clothes, shoes and purses litter the pavements of Hamra street in central Damascus, where three months ago they would have been chased off by police. Residents of Damascus’s Old City complain of instances where litter hasn’t been picked up, with street cleaners absent on certain days.

In the outskirts of Damascus, Homs and elsewhere, homeowners have taken advantage of the unrest to build without necessary government approval.

“I’ve been adding a wall around my house although the bricks have tripled in price and builders are demanding a higher wage,” says one old-city trader in Damascus. “It’s so much faster when you don’t need to get permission.”

Activists blame the government actions for the deteriorating obedience to the law, but some Syrians blame the protesters. Faced with a relentless military crackdown on protest hotspots, street protesters have widely adopted civil disobedience as a new tool of activism. This is catching on with non-protesters, too.

Residents of Douma, close to Damascus, issued a statement saying they wouldn’t pay bills for publicly supplied electricity and water as part of a civil-disobedience campaign. But one non-protester in Damascus said he doesn’t pay, either. “Officials are probably too busy to bother tracking me down,” he said.

Some citizens in Homs say they have started to buy weapons in case they need to protect themselves. The cheapest guns on the black market now go for about $800, up from about $400 a few months ago, according to Syrians and reports from Lebanese weapons sellers.

While the majority of protests are peaceful, in the town of Tel Kalakh close to the Lebanese border, residents admit to fighting government forces with weapons smuggled in from Lebanon. Both guns and rocket-propelled grenades were used against tanks after the army moved in in May, according to residents and diplomats in Damascus. Reports have emerged from other cities, too, of frustrated protesters killing security forces.

The government hasn’t commented on the growing petty crime but it has acknowledged that it has at points lost control of some areas of the country, as Hama, for example, claims it is a “liberated city.” On June 6, a senior Syrian official said that the military had “intermittently” lost control of areas around Jisr al-Shughour, a northwestern city where an army assault caused thousands of refugees to flee to Turkey.

Another fear is that the government’s forces, as well as civilians who have cracked down on dissent on the state’s behalf, could start to act of their own accord. Videos and testimonies have repeatedly highlighted plainclothed people described by protesters, activists and Syria experts as thugs paid by or loyal to the regime working alongside the army and security forces in cities including Latakia, Banias, Homs and Damascus.

The most notorious is the “shabiha,” a gang of smugglers from the coastal area, many of whom belong to the Assad clan, according to locals and diplomats.

Growing lawlessness would open space for increased chaos in the country. That would play into a government narrative that has blamed armed gangs and saboteurs for the violence and leading to the potential forming of militias or organized local revolts, analysts say.

“We are concerned if this goes on too long, because this is how militia start,” says one opposition analyst in Damascus. Non-protesters from Mr. Assad’s ruling Alawite sect report being fearful of the growing lawlessness and worry about backlash against them. Very few sectarian clashes have so far been reported.