Cr Vandervis tried unsuccessfully to push for a vote on changes to Mr Cull's appointments, announced last week, which left the mayor's most vocal critic out in the cold without a senior role.
Cr Vandervis yesterday suggested himself as chairman of the infrastructure services committee, instead of Mr Cull's choice of Cr Kate Wilson.
He also recommended first-term councillor Hilary Calvert as the city's deputy mayor, replacing Mr Cull's pick of incumbent Cr Chris Staynes.
Both suggestions failed to win support as all councillors, except Cr Calvert, instead voted to note - and thereby endorse - Mr Cull's original selections.
Cr Calvert chose to abstain rather than ''bless'' the appointments made by Mr Cull, saying she was ''slightly uncomfortable'' some of the choices did not ''totally reflect the views of the voters''.
''I feel I'm being encouraged to, in some way, bless the decision that you have made,'' she told Mr Cull.
''I'm comfortable that you're in a position to make them, but I'm not feeling it's part of my role to be involved in it.''
The exchanges came just minutes after the new council was led into the debating chamber by a lone piper, before receiving a mihi whakatau (welcome) and being sworn in before a packed public gallery.
Mr Cull, in his opening remarks, said the new term was the chance for a ''fresh start with a new mandate'', and hoped for an ''exciting and constructive'' three years ahead.
But the positive vibe started to fade minutes later, when Cr Vandervis questioned the process being used to find a replacement for outgoing council chief executive Paul Orders.
Cr Vandervis tried unsuccessfully to have an update on the process moved from the non-public to the public part of yesterday's meeting, and to extend the applications deadline, which closed on October 11.
Both bids failed after eventually being considered in the non-public section, and Mr Cull defended the recruitment process after the meeting.
He told the Otago Daily Times the process had been repeatedly endorsed by all councillors except Cr Vandervis, whose continued criticism was ''not only inappropriate and misplaced - it's just vexatious''.
Cr Vandervis denied that last night, saying he was simply raising concerns about the short application period for the role, as well as a lack of input into the advertised job description by councillors.
''I have been keen to avoid any suggestion of predetermination in the chief executive search process and I am keen to give the very widest range of candidates time to apply.
''We desperately need another truly remarkable chief executive to continue the work that [Paul] Orders has started,'' he said.
A report by the council's recruitment consultant, EQI Global, outlining the recruitment process, was considered in a non-public session yesterday but released to media after the meeting.
Earlier, Mr Cull - after being helped into his robe by Mr Orders and swearing his own oath - said it was a ''privilege'' to again serve as mayor and welcome new councillors to the fold.
He hoped the council would benefit from the new ideas and energy new councillors brought with them, saying he was ''delighted'' by the mix of experience and new blood around the council table.
The council faced important challenges, including the appointment of a new chief executive and the development and implementation of new strategies, he said.
''There's plenty of positive work to be done ... it's the ambition of many people - elected or otherwise - to leave the world a better place than they found it.''
