Refugee advocate Shane Bazzi in December was ordered to pay the now-Opposition leader $35,000 in damages and some of his legal costs over a now-deleted tweet.
The judge found the six-word tweet labelling the then home affairs minister "a rape apologist" was defamatory.
But in May three Federal Court appeal judges allowed Mr Bazzi's appeal, set aside the December order and dismissed the proceeding.
The case came back before the judges on Friday to deal with a dispute over costs.
But Mr Dutton's barrister Guy Reynolds SC successfully argued for an adjournment after an affidavit by Mr Bazzi's solicitor was provided last night.
His barrister Barry Dean said this was because an error had been discovered in relation to Mr Bazzi's legal bills.
The court was told of a $233,000 bill sent in December, which was used for assessment of costs, as well as one sent in October for $155,510.
Mr Reynolds said the latter figure was the exact amount of crowd-funding Mr Bazzi had raised for the trial.
He said he needed to cross-examine the solicitor about the costs agreement between Mr Bazzi and his lawyers.
"It may well be the case that the bills that had been provided at assessment are sham bills, with the possibility that other bills are also shams," he said.
He also raised the possibility that the actual fees agreement between Mr Bazzi and his solicitors were shams.
Mr Reynolds spoke of the prospect that Mr Bazzi was never liable for anything and the arrangement was that whatever came in from crowd- funding would be what the solicitors received.
"It may be that Mr Bazzi also needs to give evidence."
He raised the possibility that his client "does not have to pay anything at all by way of costs".
The judges said Mr Reynolds was entitled to some explanation about what the billing arrangements were and adjourned the case to November.
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