What people think Plaintiff S157/2002 v Commonwealth (2003) 211 CLR 476 means
The High Court in Plaintiff S157/2002 v Commonwealth (2003) 211 CLR 476 famously stated that s 75(v) of the Constitution entrenches a "minimum provision of judicial review" which cannot be removed by statute. Nevertheless, from time to time Parliaments enact privative clauses, which seek to protect certain decisions or purported decisions from judicial review. Plaintiff S157 is often cited in support of the proposition that where an administrative decision is affected by jurisdictional error, a privative clause will not be effective to prevent that decision from being subject to judicial review.
In Plaintiff S157, the plaintiff sought to challenge the decision to refuse him a protection visa, but was barred by the recently inserted privative clause in section 474 of the Migration Act 1958 (Cth). The plaintiff then challenged the validity of section 474, which sought to prohibit courts from successfully setting aside a decision and from issuing specified remedies.
The High Court held that section 474 was valid but largely ineffective. It also held that decisions affected by jurisdictional error could not be protected from review because they are "no decisions at all" (see Minister for Immigration and Multicultural Affairs v Bhardwaj (2002) 209 CLR 597). If a decision is affected by jurisdictional error, it could not properly be regarded as a "decision … made under this Act" and accordingly would not be covered by the privative clause in section 474.
So that's not right?
No, not quite.
What you need to remember about Plaintiff S157
Since Plaintiff S157, the High Court has continued to police the boundaries of legislative power but the law has developed in several important ways.
First, the High Court in Kirk v Industrial Relations Court (NSW) (2010) 239 CLR 237 held that the judicial review function of State Supreme Courts is similarly entrenched, provided that the ground of review is jurisdictional error. Following Kirk, while State parliaments cannot prevent State Supreme Courts from granting relief because of jurisdictional error, Parliament could deny relief for non-jurisdictional legal error.
Second, in Probuild Constructions (Aust) Pty Ltd v Shade Systems Pty Ltd  HCA 4 the High Court considered legislation that provided a means for ensuring progress payments in the construction industry by way of adjudication. Once an adjudicator made a decision it could be enforced as a judgment, and was not subject to "challenge". The High Court held that the implied ouster of the jurisdiction of the NSW Supreme Court to review non-jurisdictional errors of law on the face of the record was permissible, because the legislation did not purport to oust the NSW Supreme Court's supervisory jurisdiction to grant certiorari for jurisdictional error.
What we need to remember about Plaintiff S157 is that judicial review of privative clause decisions affected by jurisdictional error continues to be entrenched and would be very difficult for Parliament to exclude altogether. Privative clauses continue to be strictly construed, especially when they could restrict the ability of courts to review decisions that affect individual rights and freedoms (Minister for Immigration and Border Protection v ARJ17 (2017) 250 FCR 474). However, courts may afford the legislature greater leeway to exclude review for non-jurisdictional errors of law, particularly where the privative clause does not affect a person's fundamental rights.
Further restrictions on judicial review
Even where a person's fundamental rights are affected, it is possible for the legislature to restrict judicial review without entirely excluding review through a privative clause. For example, the Australian Security Intelligence Organisation Act 1979 (Cth) and the Migration Act both provide that decision-makers can issue non-disclosure certificates to prevent the disclosure of information deemed sensitive to national security. The content of procedural fairness can be reduced to "nothingness" by express language (Leghaei v Director-General of Security (2007) 97 ALD 516). This may limit an applicant's access to adverse information and affect the opportunity to respond effectively.