On television, Murray was a regular guest on The Mike Walsh Show and was a panellist on daytime discussion program Beauty and the Beast from 1996 to 2005, where she became known for her frequent volatile arguments with the show's host, Stan Zemanek.
Writing
Murray published her memoir Sheer Madness: Sex, Lies and Politics in 2010. In 2012, Murray published a novel called Goodbye Lullaby. Murray published juvenile mystery book, NO BRIDGE, NO WAY!: A Glencairn Island Mystery in 2019. Also in 2019, Murray published the autobiographical Pilgrim Souls: A Memoir.
While making a cup of tea in her husband's parliamentary office in 1985, Murray had her hands scalded when boiling hot water was sprayed onto them when a hose connected to the urn came loose. Murray rejected a settlement offer of $18,000 in 1988. In 1993, it was reported Murray had been awarded $100,000 in compensation. Murray criticised some media outlets who she says portrayed her as a villain and implied she was undeserving of the compensation amount. Administration Services Minister Bob McMullan also disputed the reported figure of $100,000 stating that the final costs were still being negotiated but said the amount would not exceed $60,000.
Sex on the desk scandal
Following initial reports in The Sun, Murray admitted during a 60 Minutes interview in 1987 to having sexual intercourse with Brown on his desk in his office at Parliament House in Canberra in 1983, and leaving a pair of underwear in an ashtray. A spokesperson for Australian Prime MinisterBob Hawke said while Murray's comments were in "poor taste" they had nothing to do with Brown's ministerial duties. The Canberra Times reported that Murray said she had never meant for her comments to be made public after being assured by a 60 Minutes producer that they would be edited out of the program. Murray's on-screen revelation continues to be referred to occasionally in the Australian media.
Defamation case against the ABC
In 1989, Murray and Brown lost a defamation case against the Australian Broadcasting Corporation. They had attempted to sue the national broadcaster after ABC Television had aired a Quantum program on 9 September 1986 which Murray and Brown believed contained defamatory implications. The pair believed the program had implied that Brown had accepted bribes from tobacco companies and that Murray had been party to an arrangement where Brown had accepted bribes. A Supreme Court jury found the program did not convey such imputations and the pair were ordered to pay the court costs of the eight-day trial.