The story that Billy Crystal tells about his "best day" of going to a Yankee game with his father is a true story from his childhood. He notes at one point that, "I still have the program." Not only does he really still have it, but he got Mickey Mantle to autograph it twice: once at the game that day and once again some 20 years later on a talk show they were both guests on.
Aside from the Yankee game story that Mitch tell, another true story from Billy Crystal's life is the wake up call from his mother on his birthday. According to Billy in the DVD Commentary, in real life, his mother would call him on his birthday at around 5 o'clock in the morning (the time he was born) and verbally re-enact the event over the phone. The rendition in the film is word-for-word the true story of Billy Crystal's birth.
Although many observers were stunned by Jack Palance's "I crap bigger than Billy Crystal!" comments at the 1991 Oscars, and didn't understand where his statement came from, Palance was actually repeating a line that his Curly character says to Crystal when they first meet at the riding camp. People forgot this line because Palance delivered it so quickly and had many more notable quotes.
The cow-giving-birth used a puppet calf, as several takes were wanted. The shot of Norman getting to his feet was real footage taken just after birth. Billy Crystal actually assisted in the delivery. Six calves were used in all, and Crystal arranged for them all to live full lives on a farm. The shots featuring Crystal were filmed in Colorado, but the shots from the same scene featuring Jack Palance were filmed in New York.
Billy Crystal's father ran a jazz label in New York and thus introduced him to many legends of the Jazz world, including Billie Holiday who took a seven-year-old Billy to his first movie. The movie was Shane (1953) featuring Jack Palance.
Billy Crystal, a notoriously die hard New York Yankees fan, wears a New York Mets cap in the film. As explained by Crystal in the DVD Commentary, he did this because the New York Mets had made a major contribution and helped out on his annual Comic Relief charity.
According to Billy Crystal in the "making of" documentary, when he first came up with the story and came up with the character of Curly, he immediately wrote down Jack Palance's name as the ideal choice for the role. No other actor was considered for the role.