True. In 1865 after a long campaign across the country Vice President Andrew Johnson was exhausted, and contracted typhoid fever. On the day of Lincoln's inauguration, he used "medicinal" whiskey to try and strengthen himself, but became so polluted that he drunkenly hobbled through his speech, "slurring his words, repeating lines incorrectly, and was interrupted by officials to administer the oath." He also used the occasion to lambaste any political opponents in attendance.(source)Too bad the motion picture camera was not invented yet. Witnesses said that friends would not let him take the reins of the horse to ride home that night. (ok, that part's false)
The first President, George Washington, travelled for seven days from his plantation home in Mount Vernon in Virginia, to the capital New York. Along the way celebrations took place in no less than five towns, including Philadelphia. One of his New York greeters was George Clinton - not the Funkadelic George Clinton, but Governor George Clinton (and later the 4th Vice President).
From one witness account, Washington appeared nervous while giving a speech to Senators just after his formal oath. He may have tried to memorize the speech without reading it, as there were long pauses.
Things were not quite as organized, believe it or not, as they are at modern inaugurations. New York's highest ranking Judge Chancellor Robert R. Livingstone was to administer the Oath of Office, but upon arriving at the balcony to proceed with the ceremony, he realized there was no bible there, and sent a messenger to a nearby Masonic lodge to borrow one. (source)
One of the worst inaugural speeches was given in 1841 by President William Harrison. It was 8000 words and took two hours in a snowstorm. It not only bored the crowd, but may have been a contributing factor in his death from pneumonia a month later.
The poet Robert Frost was asked to recite a newly written poem at John F. Kennedy's 1961 inauguration. However, being 87, and with the bright sun blinding him from properly reading his new poem called "Dedication", Frost was having trouble reading it. Richard Nixon used his own top hat to help shield the sun for Frost, but the poet gave up. He then recited a poem he was very familiar with, "The Gift Outright" perfectly.
Lincoln's first inauguration 1961 - the dome was being constructed on the Capital building
A shot of famous Pennsylvania Avenue in 1865 - Lincoln's second inauguration
From 1985, this could be the only picture of President Lincoln giving a speech at either of his inaugurations. (This is a zoom cutout from the larger view of Abe's second inaug.)The picture quality is poor, but the crowd seem to be directing their attention to the tall, bearded fellow, without the top hat.
Click to enlarge.