Kel says it's his and Kath's one month anniversary at the New Year's Eve Party but according to season one episode 7, their wedding date was in September, meaning NYE would be more like their three month anniversary.
When Kim comes to Brett's house begging for him to take her back, she says she has a "Killing Heidi hairdo". This is a reference to Ella Hooper; lead singer of the band Killing Heidi.