The tie vote between Thomas Jefferson and Aaron Burr in the 1801 Electoral College pointed out problems with the electoral system. The framers of the Constitution had not anticipated such a tie, nor had they considered the possibility of the election of a President or Vice President from opposing factions, which had been the case in the 1796 election. In 1804, the passage of the 12th Amendment corrected these problems by providing for separate Electoral College votes for President and Vice President.
Tally of electoral votes for the 1800 presidential election, February 11, 1801. Records of the U.S. Senate, National Archives.