The government was put under pressure during question time on Tuesday over its management of the Adam Brooks affair.
Labor fired all its allocated questions to Premier Will Hodgman, criticising his handling of the situation and accusing him of allowing a culture of dishonesty to brew.
Opposition Leader Bryan Green asked Mr Hodgman to rule out having Mr Brooks in cabinet in future.
Mr Brooks resigned from cabinet on Monday, four days after he misled a budget estimates hearing.
Labor and the Greens continued to question Mr Hodgman about the Crown Solicitor's audit into Mr Brooks' business email account, and whether his initial actions were strong enough.
Mr Hodgman said he found it “galling” to be questioned by Mr Green, given his history as a minister.
Mr Green resigned from the ministry in 2006 and faced two criminal trials over the Tasmanian Compliance Corporation scandal.
Mr Hodgman referred to Mr Green as being found “not innocent”, after two juries did not make a finding.
“It is staggering that he would come in here and provide free character assessments of anyone else,” Mr Hodgman said.
Mr Green said Tasmanians had been repeatedly let down by the “arrogant, secretive and dishonest government”.