1) Unresolved issues with Britain - while the war was over, and the Peace Treaty signed, tension and flashpoints still existed between us and England. There were still British troops in the Ohio country, the border with the US and Canada was disputed, our ships were being seized at sea and Britain complained about our debts still owed to the Loyalists. We sent our Chief Justice John Jay in 1794, and he negotiated a new treaty, a virtual copy of the Treaty of Paris. When he arrived, he kissed the Queen's ring, starting a firestorm of criticism from anti-federalists back home. he thought he was just being diplomatic. They thought he was acting subservient.
2) French seizures of American shipping - The US sat the French Revolution out, even though both sides of the conflict called for us to honor the Treaty of Alliance. Our neutrality angered everyone, and the French Navy began seizing our ships and keeping the cargoes. We sent negotiators in 1799, and the French demanded a bribe of $250,000 just to talk to us. Protests calling for war with France immediately took place back home, chanting "Millions for defense, not one penny for tribute".
3) The War with the Barbary Pirates in 1801 - seems like everyone was taking our boats at the time, and we were heartily sick of it. So when pirates in the Mediterranean got in on the action by charging a tax for our ships to operate there, Jefferson went to war. It was controversial at home because it was a very federalist move, and Jefferson was supposed to be the champion of the anti-federalists.