What were some important aspects of domestic affairs during Jefferson's presidency?

 

I must disagree with the above answer; as there were a number of domestic issues during
Jefferson's presidency that were of the utmost concern:

• There was
  the Essex Junto, a group of radical Federalists who saw the demise of their
  party if the territory gained in the Louisiana Purchase came into the Union. They planned to
  have New England secede from the Union under the leadership of New York. The scheme involved
  having Aaron Burr elected Governor of New York and then have him lead the effort. Alexander
  Hamilton discovered the plot, and exposed it, which ruined Burr's reputation. It was as a result
  of this dispute that Burr challenged Hamilton to a duel in which he killed him.


• There was the Tertium Quid, a group of radical Republicans who
  opposed any move of Jefferson's which they considered "liberal." They were the first
  of several third party movements in the U.S.; none of which were successful.


• There was the Burr conspiracy in which Aaron Burr and General James Wilkerson planned
  to have Louisiana secede from the U.S. and form their own Empire. The plot failed, and Burr was
  tried for treason. The trial was presided over by then Chief Justice John Marshall who would do
  anything to embarrass Jefferson. Marshall adopted a strangely strict interpretation of the
  burden of proof for treason which not only resulted in Burr's acquittal, it set a difficult
  precedent for future treason trials. At the same trial, Jefferson refused to honor a subpoena
  from Burr's attorneys, thereby laying the groundwork for executive privilege.


• There was the Embargo Act, intended to keep America out of the war with France and
  Britain. It ended up ruining the American economy.
• Most importantly, the
  Supreme Court of Marbury vs. Madison was issued during Jefferson's
  presidency. This all important case established the principal of Judicial Review.


• Contrary to the position of the earlier post, Jefferson's purchase of Louisiana
  did not result in any great debate over
  Constitutional interpretation. Jefferson construed his power to make treaties in the name of the
  U.S. as sufficient to justify the purchase; a strangely broad construction. He justified his
  actions by writing:

the good sense of our
country will correct the evil of loose construction when it shall produce ill effects.

• All of this goes without mentioning the efforts of Louis
  and Clark, and the Jefferson's enormous popularity after doubling the size of the U.S.