Domestic abuse campaigners and MSPs across the political spectrum have called on Walker, 71, to resign his seat after he was convicted yesterday of 23 charges of assault against three ex-wives and a teenage step-daughter.
He will be sentenced next month but faces no more than a year in jail, too short a term to disqualify him automatically from serving as an MSP.
Labour and Conservative MSPs demanded to know how he had been chosen to stand for the Holyrood seat of Dunfermline, which he won with a majority of 590 over Labour in 2011.
The Herald's sister paper, the Sunday Herald, revealed last year that the SNP was warned of his violent past by Rob Armstrong, the brother of Walker's third wife, Diana Walker, whom the shamed MSP assaulted on several occasions.
Mr Armstrong passed information to Deputy First Minister Nicola Sturgeon's constituency office, which was in turn relayed to senior officials at party HQ in 2008 after Walker became a councillor in Fife.
Ruth Davidson, Scottish Conservatives' leader, said: "A family member of one of Bill Walker's victims informed the party hierarchy of serious allegations of violence made against him, yet the party still saw fit to put him in Holyrood under the SNP banner.
"The SNP leadership now has some big questions to answer in relation to the way in which they have handled this whole unsavoury episode."
Labour MSP Claire Baker said: "Nicola Sturgeon and the SNP leadership must now tell the people of Scotland who knew what and when."
In its first detailed statement on the case since charges were brought, the SNP insisted the party had tightened its vetting procedures for would-be MSPs following an internal inquiry.
An SNP spokesman insisted Ms Sturgeon was not made aware of the meeting in her office, but added: "The matter was considered by a member of staff at SNP headquarters and reasonable enquiries made, but there was no evidence of any complaint in law or legal proceedings into Mr Walker's conduct, and the inquiry was closed.
"The SNP President, Ian Hudghton MEP, carried out an internal review of assessment procedures last year, after Mr Walker's expulsion.
"While the onus was clearly on Mr Walker to disclose information, which he did not do, in a significant strengthening of our procedures any potentially relevant information made available to party headquarters will be passed directly to the Election Committee convener for assessment."
He said the party had also expanded the number of questions it asked about matters that "could cause concern," including a requirement to disclose all previous charges, proved or not.
Walker was suspended by the SNP when allegations of domestic abuse were revealed in the Sunday Herald and was later expelled.
He has continued to serve as an Independent MSP at Holyrood, ignoring previous calls to step down.
Walker was found guilty at Edinburgh Sheriff Court of 24 charges in all over a period of nearly 30 years.
Delivering her verdict, Sheriff Katherine Mackie said: "There was evidence showing the accused to be controlling, domineering, demeaning and belittling towards the three complainers, his former wives.
"The evidence also showed him to be untrustworthy, disloyal and unfaithful towards others including his present wife."
Meanwhile, Willie Rennie, Scottish Liberal Democrats' leader, joined Labour and the Conservatives in calling for him to quit Parliament, saying: "He has to go and he has to go now."
Patrick Harvie, the Scottish Green Party leader, said: "Walker should resign immediately."
Walker, who had denied the charges, made no comment as he left court.
His solicitor, Russell McPhate, said: "Mr Walker is obviously disappointed to be convicted of all the charges today. The verdicts, in particular the comments of the sheriff, will be very carefully considered."