What was significant about the transfer of power after the election of 1800?

While the election of 1800 was a closely fought battle, and the presidency of Thomas Jefferson had long-lasting repercussions on the nation, one incident stands out during the actual transfer of power from Adams to Jefferson: Adams's so-called "Midnight Judges."
In the waning days of Adams's presidency, he signed into law a bill that doubled the number of circuit courts, creating a number of vacancies in high-ranking judicial positions. He spent his last days in office filling those vacancies personally, supposedly granting judgeships up until midnight of his last day in office. 
When Jefferson refused to recognize these appointments, the legal battle ended up in the Supreme Court. That case, Marbury v. Madison (Marbury was one of Adams's judges; Madison was secretary of state), was the first case in which the Supreme Court asserted its power to declare a law unconstitutional. This precedent redefined the legal landscape of legislation in the United States.