the census gathers data on a consistant basis, nationwide at specified intervals. Everyone gets the same questions, at the same time (give or take with the on-line version). And because all the responses are given under the same conditions and at the same time, unrealted data can be linked (for example, income with place of living; english speaking at home (or not) with other metrics).
Whilst the form is consistent people are not. The census relies on the person completing it to be literate, choosing to take it seriously and answer honestly.
There will be people who don't have the required literacy skills to complete it correctly and there will be those that don't complete it at all. Most will do their best, whilst some will lie.
There is clearly a lot of concern from the census organizers re possible insincere answers, given the ads they are running on the radio currently.
The ABS opted to ignore all those who ticked "other" then wrote "Jedi Knight" on the Religion question in the last couple of census'. Maybe some of those people actually do believe in the force, the official religions listed have some equally crazy ideas.
The census isn't necessarily going to be more accurate than other government sources of information. Which is why comparing and combing census data with other government data (or for commercial use company held data) often gives better insights.
Income is one question which suffers from accuracy concerns. Some people are very distrustful of government, this may lead to them under reporting income on census. The more lazy types will specify a rough income from memory which may be a fair way off the actual mark (especially if they confuse before/after tax). And those working in illegal cash in hand jobs or avoiding tax, aren't any more likely to be honest on the census than they are on their tax return.
The ATO has more nuanced income data, which they do anonymize and make available. Even for those who haven't filed a tax return, the ATO received data due to TFN being captured by banks, employers, government agencies paying benefits, super accounts, shared schemes etc.