In a 1969 article from Masque magazine, THE INCIDENT was listed as being banned by the Australian Censorship Board.
snip, snip, snip, snip
Masque, June-July 1969
The use of restrictive certificates [in New Zealand] has meant that films which would not be passed for general exhibition may still be passed for an adult audience. Thus THE INCIDENT, banned in Australia, was passed with a restrictive certificate in New Zealand, with only one cut.
An outstanding American film by Larry Peerce, it shows the behaviour of a group of people trapped on a subway car by two young hoodlums. The film is a brilliant expose of the roots of violence in American society, and it is tragic that the Australian public have been deprived of the chance to see the film for themselves. I am surprised that more publicity has not been given to the banning of THE INCIDENT, which is a most important social statement.
In August 1970, THE INCIDENT was resubmitted to the Censorship Board. The 8655-feet (96:10) print was passed with a 'Suitable only for Adults' rating.
Information provided by Shane Harrison
My understanding is that one cut made to THE INCIDENT for it to be rated in August 1970. This was because a banned film could not be resubmitted in the same version for 5 years after in was last seen by the Censorship Board. It could be submitted for an appeal on the ban in the same version, but due to expense most studios bypassed this and resubmitted a cut version as happened with THE INCIDENT.