I figure by next week at this time, everyone will be all inaugurationed out, so I'm getting to you early with the trivia. Plus, this way you can impress people with your presidential knowledge when people at work (or school) are talking about the details.
1. Jimmy Carter's inauguration was distinctive for a few reasons. First of all, he was the first president to be sworn in by a nickname. Second, his Inauguration Day parade included a Macy's Parade-like balloon of a peanut to celebrate his past. And third, his wife, Rosalyn, was also the only First Lady (in recent history, anyway) to wear an old gown for the swearing-in ceremony. Seeing no reason it shouldn't be worn again, she wore a dress she had worn to a gubernatorial ceremony in Georgia.
3. Calvin Coolidge had some interesting people swear him in as president.
The first time, after Warren G. Harding died in office, Coolidge was sworn in by his notary public dad. They were at a farm in Vermont and had to conduct the whole thing by kerosene lamp. The second time, he was sworn in by former president William Howard Taft, who was chief justice of the Supreme Court at the time.
4. Thomas Jefferson walked to and from his own inauguration.
5. Warren G. Harding was the first to arrive at his inauguration via car.
6. When Andrew Johnson was inaugurated as vice president, he was totally trashed. He was very ill from typhoid fever and drank whiskey to try to numb the aches and pains a little. Except he overdid it and ended up slurring his way through his oaths. Then he tried to swear in the new senators, but got too confused and had to let a Senate clerk complete his duties instead. "The inauguration went off very well except that the Vice President Elect was too drunk to perform his duties and disgraced himself and the Senate by making a drunken foolish speech," Senator Zachariah Chandler reported. "I was never so mortified in my life, had I been able to find a hole I would have dropped through it out of sight."
8. Barack Obama may be using the same Bible to take his oath as Abraham Lincoln did, but Teddy Roosevelt still has one up on him: he actually wore one of Lincoln's rings. John Hay, Roosevelt's secretary of state, was also Abraham Lincoln's private secretary (he was only 22 at the time) and was there when Lincoln was assassinated. Hay was given the ring by Mary Todd Lincoln and let Roosevelt use it in his 1905 inauguration.
9. The Adams presidents were apparently sore losers. When their successors were inaugurated, both John Adams and John Quincy Adams made it a point to be otherwise occupied far out of town.
10. In his inaugural address, James Buchanan announced that he wasn't going to run for re-election. He was true to his word, and maybe that's for the best: he's continually ranked as one of the worst presidents the U.S. has ever had.