These issues are all challenges for inflation measurement, but they're also challenges of communication for central banks. To meet this challenge, the best response is transparency. The inflation measure that the Bank is mandated to target is not, strictly speaking, a measure of the cost of living, but it is close to it.
In practice, measures of increases in the cost of living are similar to CPI inflation (Graph 2). That similarity is important for social licence: if we are going to be mandated to target something, that target should be relevant to the welfare of the Australian people.