Abedi, 22, was reported to police and security as acting suspiciously in the minutes before he detonated his bomb but no action was taken.
One member of the public said he was “fobbed off” by security after spotting Abedi appearing to pray while wearing a large back pack less than an hour before the explosion at 10.31pm on 22 May 2017.
Another approached a British Transport Police (BTP) officer to point out Abedi. The officer cannot now recall the conversation.
Paul Greaney QC, counsel to the inquiry, told the first day of the public inquiry that experts had been asked to look into the security at the arena that night.
He said that "of considerable importance, the experts consider, on the basis of the information currently available to them, that, on 22 May, there were missed opportunities to identify Salman Abedi as a threat and take mitigating action."
He said that the experts concluded: "If the presence of a potential suicide bomber had been reported, it is very likely that mitigating actions would've been taken that could have reduced the impact of the attack.
"This is because there was sufficient time between Abedi first being spotted by, and also reported to [security] staff and his attack to effectively react."
Mr Greaney said: "The evidence about these potential missed opportunities will need to be considered with the greatest possible care."
He said whether there were "missed opportunities" to prevent the attack or reduce its deadly impact would be a key consideration for the inquiry, which began on Monday.
Loved ones of the 22 people who died in the bombing stood in silent remembrance as the names of the victims were recited at the opening of the hearings.
The sombre proceedings began with Mr Greaney QC, counsel to the inquiry, reading the names of each of those murdered by Abedi on 22 May, 2017.
Sir John Saunders, a retired High Court judge, is leading the probe examining events before, during and after the attack at the end of an Ariana Grande concert.
Abedi, surrounded by a throng of elated youngsters leaving the show, exploded his shrapnel-packed rucksack bomb, sending thousands of nuts and bolts shredding everything in their path.
Witnesses A, who had taken his daughter to the concert, said in a statement he saw a man matching Abedi's description who “looked out of place” and was acting suspiciously, the inquiry heard.
He asked the suspect, "What are you doing?" but the man thought to be Abedi replied that he was waiting for somebody.
Witness A then spoke to Mohammed Agha, employed by venue security firm Showsec, at 10.14pm but said he was "fobbed off", the public inquiry heard.
Mr Agha spoke to a colleague, Kyle Lawler, eight minutes before the bomb went off and Mr Lawler is then said to have tried to radio his security control, but could not get through.
Mr Lawler said in a statement he saw the man get up and start walking towards the arena entrance, as youngsters began streaming out to meet waiting parents.
He added: "I just froze and did not get anything out on the radio. I knew at that point it was too late."
Another opportunity arose when witness Julie Merchant approached British Transport Police (BTP) officer Jessica Bullough, about 32 minutes before the deadly bombing, to point out Salman Abedi.
Earlier, formally opening the inquiry, Sir John said: "This is an exercise in establishing the truth.
"If I conclude things went wrong then I shall say so, but we are not looking for scapegoats. We are searching for the truth.
"The explosion killed 22 people, including children, the youngest was eight years old.
"Salman Abedi blew himself up in the explosion but he intended as many people as possible would die with him."
Sir John said some evidence must be heard in secret to prevent further similar terrorist attacks.
Abedi was known to the security services, and a senior MI5 officer, known only as witness J, is expected to give evidence to the inquiry later this year.
The bomber's brother, Hashem Abedi, now 23, was last month jailed for life with a minimum 55 years before parole, for his part in the deadly bomb plot, which left hundreds of other people injured.
Some evidence, involving information judged to be potentially of use to terrorists, is subject to restriction orders, and those hearings will be closed to the public.
The most sensitive evidence is likely to be heard at closed hearings, with both press and public excluded because of the risk to national security.