In December last year he was arrested and charged with using a carriage service to transmit publish or promote abusive material.
Today the 40-year-old pleaded guilty. He will be sentenced in September.
Outside court, Finch's lawyer Paul McGirr said some of the charges had been withdrawn and referenced his client's mental health problems.
"We just as that everyone remember there's mental health issues at play, and we have to respect that at this stage," McGirr said.
"We're not going to say anything more before sentence and we know you'll respect my wishes and also my clients bearing in mind the mental health issues I've alluded to which he's get ongoing treatment for."
Readers seeking support and information about suicide prevention can contact Lifeline on 13 11 14. National Domestic Violence Service: 1800 RESPECT (1800 737 732). If you are in immediate danger call Triple Zero (000).
