The Supreme Court had the power to do what it wished, so long as the question is properly raised, it came to a decision it believed within its powers and the law and Constitution, and it could find somebody to enforce its decisions.
In the case of most of the other midnight judges the process had been
- Outgoing president Adams had appointed them
- The outgoing Senate had approved them
- The acting Secretary of State John Marshall had delivered their commissions
Point 3 had failed to happen for William Marbury due to lack of time, and he therefore brought his case against new Secretary of State James Madison to get his commission. Although the Supreme Court then decided (with John Marshall as Chief Justice) that Marbury should have received his commission, they also decided that the Supreme Court could not order Madison to act.
There were no grounds to challenge other appointments where the commissions had been properly delivered.