Here are some one liners...
A Mutiny for Higher Pay -- Several mutinies lead to reform of the Royal Navy.
Millions for Defense, not a Cent for Tribute. America's First Undeclared War -- When negotiations break down with France, America does something short of war... a quasi war.
In Other News -- USS Constitution launches, The flag of Italy is made, The German National Anthem has its beginning and Admiral Nelson has his arm amputated.
A Mutiny for Higher PayMutiny on a British warship is an exceedingly foolish thing to contemplate, but driven by a lack of food and no pay raise since 1658, the sailors currently at the Spithead anchorage conspire to protest their treatment. They stage a two-week work-stoppage. Officers are prevented from leaving, except for a hated few. Otherwise, normal respect for officers is maintained. The sailors promise that if the French set sail, they will suspend their protest and fight. Otherwise, the sailors have taken an oath amongst themselves not to cave until their central demands are met. This strike is seen by the English government and the man-in-the-street as endangering the safety of the nation. Nevertheless, the demands are met and the sailors are pardoned. It does not go so well with the mutiny at Nore anchorage. The leader, Richard Parker, makes sweeping demands, including peace with France. After a short time, his fellow sailors start deserting. The mutiny collapses and Parker is hung along with 29 co-conspirators. Several other mutinies occur this year which result in reforms to the Royal Navy, and the prohibition of (secular) oaths that conflict with the duties of a sailor. Religious oaths are trickier and remain under discussion.    
Millions for Defense, not a Cent for Tribute. America's First Undeclared WarThe USA has run up a heck of a bill with France but does it still owe the money? The original French monarchy is gone and the government of France keeps changing. They are currently on their 3rd government depending on how you count it. Frankly it is a dictatorship. It is also interdicting American shipping, seizing over 300 American merchant ships. A new treaty must be negotiated, but negotiations cannot start because certain French officials want a hefty bribe first. President John Adams recalls his negotiating team. His political opponents assume that the negotiations have failed because his incompetence, so they demand the French dispatches. Adams is forced to turn them over, but he substitutes the letters X, Y, and Z for the names of French officials demanding bribes. It becomes known as the XYZ Affair. By the rules of the Senate, Thomas Jefferson is required to read the dispatches out loud. Abigail Adams delights as she watches him squirm. The public is outraged. They shout, "Millions for defense, not a cent for tribute." John Adams manages to avoid outright war. He gets funding for finishing the Navy frigates, and runs his own Quasi-War... an undeclared war with France. This war will continue until 1800.     
In Other News
- The flag of Italy is first used. After the Milan region is conquered by Napoleon, he has a new flag made using the old Milan colors plus the green of the Milan guard. It is styled after the French flag, naturally. 
- Deutschland über alles (Germany above all else) Joseph Haydn adapts a traditional melody for a song to honor Emperor Franz. It will one day become the National Anthem of Germany. After World War 2, they will skip the "Germany above all else" stanza.