In Bill James's Abstracts from the 1980s, Rob Neyer (who then worked as James's assistant) would note a story from a player's biography or Baseball Digest and attempt to track down the details of the tale. Neyer called his reports "tracers". Since Dan Shaughnessy, Francona's co-author, acknowledged that "Books like this are impossible to write today without a website like baseball-reference.com", I was curious how the various stories checked out.
(Note: My noting of any inaccuracies in the following remembrances is not meant as a criticism of the book. I am enjoying the book, and I fully expect to enjoy the entire book, especially the 2004 section. Consider this post an exercise in picking nits.)
A couple of days later [after his big league debut], Little Tito led off, went 0-5, and got thrown out at the plate in a 1-0 loss. (page 25)
Francona made his debut with the Expos on April 19, 1981 in Houston and Shaughnessy gets the details of Tito's pinch-hit appearance correct (he grounded out to first). The game in question here happened in Atlanta on April 23, four days later. Francona did lead off and he did get thrown out at the plate. But he went 0-4 (he had five plate appearances) and Montreal lost the game by a 2-1 score.
In parts of ten seasons in major league baseball, he hit .274 with 16 homers and 143 RBI, playing 708 big league games for the Expos, Cubs, White Sox, Indians, and Brewers. (page 26)
All of the numbers are correct, but Francona never played for the White Sox. He did, however, play 102 games for the Cincinnati Reds.
"There's one other stat that nobody knows about," said Dustin Pedroia . . . "He is the only player with a minimum of 1,000 plate appearances to never work an 0-2 walk. How awesome is that? He had no fight in him. None! That's unbelievable." (page 26)
I don't know if Francona is the only player to do so, but it's true. He did not draw a walk in any of the 72 plate appearances in which he fell behind in the count 0-2. If Pedroia loved that factoid, he'd be ecstatic to know that Francona also never worked a walk after a 0-1 count (which happened 196 times)! As Shaughnessy notes, "He swung at almost everything."
"When I got to the dugout [on his first trip to Fenway Park] and looked out and saw the park, I thought I'd died and gone to heaven. I hit against Mike Boddicker in that series. And against Roger Clemens. I pinch-hit, and I fouled off a ton of balls. He finally got tired of it and threw one about 100 miles an hour, and I struck out." (page 27)
Francona was with Cleveland in 1988, and visited Fenway for a series on September 9-10-11. He DH'd against Boddicker in the first game. In the second game, he pinch-hit against Clemens in the eighth inning. He struck out on four pitches, fouling off one pitch (called strike, swinging strike, foul, swinging strike).
Francona enjoyed his final days in the majors playing for young Brewers manager Tom Trebelhorn. He knew he was the 25th man on the roster, so he did all the little things. He pitched an inning against Oakland ("I struck out Stan Javier on a knuckleball") when Trebelhorn was out of bullpen arms. (page 28)
On May 15, 1989, Francona pitched the eighth inning for the Brewers against Oakland. The A's were up 12-2. He retired the side in order, striking out Stan Javier for the third out.
"We'd had a dispute with Ken Kaiser early in the  season," Francona remembered. "About two months later, he was working home plate for one of our games against the White Sox. I was sent up to pinch-hit, and first base was open, so they ordered an intentional walk. Kaiser and I were yelling at each other the whole time. Every pitch. Carlton Fisk was catching, and he couldn't believe it. Finally they threw ball four, and as I was starting down the line to take my base, Kaiser said, 'I make 3,000 calls a year!' and I hollered back, 'And 2,000 of them suck!' That did it. He tossed me." (page 28-29)
Francona was intentionally walked three times in 1989, one of which came in the eighth inning against the White Sox, on July 15, 1989. However, there are four things wrong with that game: Francona started as Milwaukee's designated hitter, Fisk was not catching (he was Chicago's DH that day), Kaiser was not behind the plate (in fact, he was not part of the umpiring crew at all), and Francona was not ejected.
I saw that Francona drew a non-intentional walk against the White Sox on May 2, 1989, but Fisk did not play that day and Kaiser was not in that umpiring crew, either.
Going through the other games in which Francona walked, I found July 9. Francona entered a game against Baltimore in the sixth inning as a pinch-runner for Milwaukee's DH. Francona batted in the seventh and with a runner on second base and two outs, was intentionally walked. Ken Kaiser was the home plate umpire. There is no note of an ejection in the box score, but Mike Felder pinch-ran for Francona after the BBI. It's quite possible this was the game Francona was referring to.
Late in the  season, he used the oft-limping Francona as a pinch-runner.
"That was Trebelhorn being nice," Francona remembered. "With about ten games left, I'd mentioned to a couple of guys that I needed to get in eight more games to trigger a $25,000 bonus. The next day I pinch-ran. And again for another bunch of games. I remember thinking that Trebelhorn was crazy, but then I pinch-ran in the next-to-last game of the season and got my number. I mentioned something to Trebelhorn about it, and he said, "It's my way of saying thanks.' That went a long way with me." (page 29)
Francona was last used as a pinch-runner for the 1989 Brewers on July 28, so this story cannot be completely accurate. Francona played sporadically through August and September, but then (with about ten games remaining in the season) Trelbelhorn started Francona in four consecutive games, and five out of six games (Games 151-152-153-154-156). Francona also started the final game of the season, so he played in seven of the final 11 games, which may have triggered a bonus clause.
In April 1990, Francona stepped to the plate in the eighth inning of an 18-0 Brewers rout of the Red Sox. It was Marathon Day in Boston, the only 11:00 AM start in baseball every year. Facing right-hander John Leister, Francona went out on a sinking liner to center. A few days later Trelbelhorn called him into his office and told him he was being released.
The fly ball in Boston was Terry Francona's final major league at-bat. He finished his playing career on the same diamond where his dad made his big league debut after meeting Ted Williams in 1956. (page 29)
The details of Francona's last AB on April 16 are correct. (And his father, Tito, did make his debut at Fenway, on April 17, 1956.) However, Terry Francona did not finish his playing career at Fenway. He appear in one additional game, in Texas, pinch-running for Dave Parker on April 19. He was three days shy of his 31st birthday.
(On May 5, Francona signed with the Cardinals as a free agent. He played 86 games with the Cardinals' AAA team in Louisville, batting .263/.291/.379. He tried to come back in the spring of 1991, but additional injured ended his professional career.)