In domestic affairs, the US was relatively quiet during Jefferson's time as president. As the first Democratic-Republican president, Jefferson did some things to reverse the policies of the Federalists, but not as many as might have been expected. Mainly, he ended the excise taxes that caused the Whiskey Rebellion, reduced the size of the judiciary, and also reduced the size of the army and navy.
The main domestic controversy during Jefferson's time was about whether he could buy the Louisiana Purchase without approval from Congress. This was a partisan issue that was couched in Constitutional terms. The Constitution did not say that a president could buy territory from a foreign country so Jefferson's proposal led to a debate over whether the Constitution should be interepreted strictly (the president could only do what it specifically said he could) or loosely (allowing him to do things so long as the Constitution did not forbid them).