Nicola Sturgeon said sorry to Rob Armstrong, the former brother-in-law of Walker's third wife, after the SNP failed to act on documents he gave to her office.
Although Walker was elected as the SNP MSP for Dunfermline in 2011, the Nationalists were warned about him three years earlier
Armstrong, a retired pilot, met one of Sturgeon's constituency assistants in Glasgow and presented her with a dossier on Walker's past. The documents included an old newspaper article on Walker, a critical court judgment and a hand-written affidavit.
In the affidavit, Walker responded to claims he smacked his then teenage stepdaughter on her bare bottom: "After no more than [waiting] 15 minutes she did receive her 'punishment', one smack on each buttock with a slipper, with her navy blue knickers on."
The opening paragraph of the newspaper report, from 1991, stated: "This is William Walker, a child disciplinarian who has admitted hitting his wife. He has been described as a bully and a tyrant by a judge. He has admitted hitting his stepdaughter with a saucepan."
Despite Sturgeon's aide informing party headquarters about the information, Walker was selected as a candidate. The failure to act prompted Armstrong to call for the resignation of SNP chief executive Peter Murrell, who is married to Sturgeon.
It has now emerged that two SNP heavyweights have spoken to Armstrong since Walker's conviction last month,
Sturgeon had a lengthy telephone conversation with the whistleblower and apologised for the fact Walker had been selected.
Armstrong also had an hour-long meeting at party headquarters with SNP director of communications Kevin Pringle, who ran through changes that have since been made to the party's vetting procedures.
Armstrong told the Sunday Herald: "The apology was very welcome and I felt it was sincere. I have accepted it."