Justice John Burns began hearing the appeal in the ACT Supreme Court on Wednesday afternoon.

In July, a Canberra magistrate found Slipper had acted dishonestly and knowingly caused a risk of loss to the Commonwealth when he misused his travel entitlements to take to visit Canberra region wineries in 2010.

The former parliamentary speaker was sentenced to 300 hours community service and ordered to repay $954.

But lawyers for Slipper appealed the conviction on 13 grounds and asked to have the guilty verdict set aside.

The appeal grounds include that the verdicts had been unsafe as the magistrate had drawn inferences of dishonesty not available on evidence, failed to have regard to procedures in place to repay monies claimed, erred in refusing to allow cross-examination of a Department of Finance official, and erred in finding evidence established beyond reasonable doubt that Slipper had travelled for "private purposes".

Slipper's legal team had also sought to put further evidence before the court, in the form of two news reports published by Fairfax Media.

One article, from October 2013, revealed Prime Minister Tony Abbott had been allowed to pay back expenses he had claimed to attend a wedding after advice from the Department of Finance – the body that oversees the parliamentary entitlements scheme.

Slipper's lawyer, Kylie Weston-Scheuber, said the articles showed there had been uncertainty – even among those employed to police it – about the boundaries of the scheme.

But Justice Burns told Ms Weston-Scheuber that he was against her.

The Commonwealth Department of Public Prosecutions has previously signalled it would oppose the application.

Ms Weston-Scheuber said the magistrate had incorrectly approached the reasoning exercise in deciding guilt.

The lawyer argued the magistrate had assumed because Slipper had falsely filled out the cab charges that he had done so intentionally and therefore had a reasonable belief that he would cause a loss to the Commonwealth.

But Ms Weston-Scheuber said evidence showed Slipper had a tendency to provide incorrect information on travel forms.

She said he may also have filled in the cab charges for a range of other reasons, which were not exclusively to dodge his entitlements.

Ms Weston-Scheuber also argued the prosecution had not proven her client had not conducted parliamentary business and therefore breached his entitlements while on the trips.

The appeal will continue on Thursday with submissions from the Commonwealth DPP.