As mllwswpr has so aptly mentioned, the presidental election of 1800 was riddled with problems. Some were solved with Amendments, some with precedent. As elections go, the election of Jefferson was one of the most important.
The Federalist party manged to have two presidents in office before dissolving. Altough he wasn't initially, George Washington favored the Federalist party and is regarded as the first Federalist president. The second was John Adams. Up until 1799, a single party had been running the newly formed United States of America.
In 1800, Thomas Jefferson, a Democratic-Republican, was elected to succeed John Adams, a Federalist. For the first time in American history the presidency changed hands. In present day America the changing of the guard is important, however not violent. However, the precedent for regime change has seen violence. History is riddled with hostile government takeovers as power hungry persons seize power or refuse to give up authority. A good example in the present would be the various African nations whose governments are constantly in turmoil. Thomas Jefferson saw this as the first real test of the new democracy. The democratic experiment and the future of the new Constitution depended on a peaceful revolution. Fortunately, the precedent was set for the Democratic-Republicans to take office in Jefferson's "Revolution of 1800."
Not everything was so easy though. With the removal of the Federalist party from office, Adams tried to hold on to as much power for the Federalist party as possible. The legend goes that John Adams stayed up until midnight before Jefferson took office to sign numerous appointments. These so-called "Midnight Appointments" attempted to fill any vacant government positions with Federalist party members. Before civil service reform, the president was allowed to appoint to any government position whomever he wished. "To the victor goes the spoils."
Jefferson took office with many newly appointed Federalist employees. Jefferson attempted to block these appointments by ordering that the Secretary of State
, James Madison
, refuse to deliver the commissions. A man by the name of William Marbury
sued James Madison for his commission. The final result was the most important legal case in American history, Marbury v. Madison
. This case set the precedent for judicial review