A 12-year-old girl has been stabbed and two police officers have been allegedly assaulted in separate incidents in Adelaide on New Year's Eve, authorities say.

SA Police Assistant Commissioner John De Candia said 72 people were arrested and 10 were reported for offences overnight across the state.

But he said overall, police were "really pleased with the behaviour of the majority of people".

Assistant Commissioner John De Candia said one of those incidents included a girl who was found with a single stab wound to her abdomen at the Salisbury interchange just before 7pm on Wednesday.

A 15-year-old Davoren Park girl, a 15-year-old Pooraka girl and a 14-year-old Craigmore girl have since been charged with affray and aggravated assault.

The Davoren Park teen, who police will allege stabbed the victim, was further charged with assault causing harm.

All three were refused police bail and will face the Elizabeth Youth Court at a later date.

The 12-year-old girl was found with a stab wound to her abdomen. (ABC News: Will Hunter)

"They are all known to each other and it appears to be as a result of [an] ongoing dispute between those people," Assistant Commissioner De Candia said.

"Fortunately, the young girl is not seriously injured and the other three will appear in court on Friday."

He said he "can't say specifically" whether officers were conducting handheld metal detector searches before the alleged stabbing at the Salisbury interchange and that police undertook wand searches "at a variety of locations" overnight.

Police were given expanded powers earlier this week to search people for weapons on all Adelaide public transport services, and at stations and interchanges.

"It's unrealistic for us to be everywhere — the public won't want us to be everywhere and to be wanding everyone coming into every train station or transport hub," Assistant Commissioner De Candia said.

"We can't always be at the right place at the right time but, fortunately in this case, it was a really quick response to be able to get the other girls at a nearby train station and they've been arrested."

Disturbance at Underdale

The assistant commissioner also said two people had been charged after two police officers were allegedly assaulted while trying to break up a fight on Hardys Road at Underdale.

He said police responded to reports of a stabbing at about 11pm on Wednesday but when they arrived, the officers were "confronted by a group of 20-odd people who were quite agitated".

"There were a number of females fighting [and] police tried to break that up, with one of the officers being struck from behind to the side of the head," he said.

He said the officers called for assistance during the "commotion" and later found another person "in possession of a kitchen knife".

Assistant Commissioner John De Candia says the Underdale incident is under review. (ABC News)

A 54-year-old man and a 17-year-old girl, both from Underdale, were arrested and charged with assaulting a prescribed emergency worker and hindering police.

The pair were bailed to appear in court in February.

A 28-year-old Cheltenham woman was cautioned and released from police custody.

Assistant Commissioner De Candia said the incident would be reviewed because the officers had used pepper spray.

"All those matters get reviewed … but I'm certainly comfortable with the degree of force and reasonableness of the action taken by the police last night," he said.

"Again, it's just that example of police and emergency services doing their job — no one expects to come to work to be assaulted."

Assistant Commissioner De Candia said a senior officer had reviewed body-worn vision of the incident and "backed the actions of the officers that went last night".

He said no one was arrested over the initial report of a stabbing.

"There was someone with minor superficial wound that the SA Ambulance Service were able to check out," he said.

"Certainly at the time last night, [people there] were extremely uncooperative with police," he said.

"It may be something that, once they sober up or calm down, they might … choose to report to police or not."

Dozens of illegal fireworks set off

Police also issued 225 expiation notices for "a wide variety of offences from drinking in a dry zone, disorderly behaviour" to drug possession matters, Assistant Commissioner De Candia said

"The stats are very similar to last year with the number of arrests and reports, he said.

"But there was certainly an increase in the number of expiation notices issued."

Police arrested 72 people overnight. (ABC News: Che Chorley)

Assistant Commissioner De Candia said police were also seeking witnesses after a male allegedly grabbed and kissed a teenage girl at Semaphore Jetty at about 11:40pm on Wednesday.

"It's concerning and completely inappropriate that a male has grabbed a teenage girl and kissed her  … the identity of the male was not known at this stage," he said.

Meanwhile, the Metropolitan Fire Service responded to at least 13 incidents believed to be caused by illegal fireworks, but Chief Officer Jeff Swann said he suspected "the total number may be higher".

"It is disappointing to see the number of incidents attended by the MFS this New Year's Eve caused by illegal fireworks, placing unnecessary strain on emergency services and increasing risk to community safety," he said.

"The incidents ranged from smouldering fires to grass fires and typically required the response of one or two fire appliances — between four to eight firefighters.

"Thankfully, crews were able to respond quickly and extinguish the fires before they spread or caused further damage and impact to the community."