This was a book that was clearly a collection of individual stories of various length, possibly edited for consistency but not “fixed up”.
All These Earths, a 1978 novel by F. M. Busby, published under these covers; summarized thusly by Risingshadow:
Star pilot Woody Pearsall's return home to Earth had suddenly become a nightmare. His wife, his commander, even the base records all said he'd been dead for over five years. The Skip Drive which had made interstellar flight possible had an unexpected side effect – shifting him to an alternate Earth!
It was originally published as a series of four stories, Busby's Jay Pearsall (Elwood Jay "Woody" Pearsall) series, comprising:
"Pearsall's Return", a novelette from Worlds of If, July-August 1973, available at the Internet Archive;
"Search", a novella from Amazing Stories, December, 1976;
"Nobody Home", a novella from Amazing Stories, July 1977;
"Never So Lost . . .", a novelette from Amazing Stories, October 1977.
In it, FTL travel is invented that works by suppressing the number of appearances matter normally makes as it undergoes motion.
"The trick is that space and time are quantized. If you don't know what that means, wait and ask me later. Mainly, the Universe doesn't exist continuously. It pulsates—appears and disappears at a rate much too high to measure. So when you move, you do it by vanishing at one point and reappearing at the next—normally.
"Ordinarily, in moving we hit every point along the way. Skip Drive suppresses our appearances at most of those points; we beat light-speed because it's the ins and outs that use up time and energy, not the motion itself."
They eventually figure out that this gives uncontrolled travel sideways in time as well! The ship comes back to a universe with a slightly different history than the one it left.
"Nice, isn't it? We thought we had the Universe by its short hairs. So we sent you out at top Skip—well over a thousand, I believe—and instead of coming back to where you once belonged, you came here instead.
"Kunda told me why. There are more worlds than one—more than we could count, I expect. There have to be, to explain what's happened. They run side by side in time—in the ordinary way you'd stay in your own rut—no way to get out of it. But on high Skip Factor, with the checkpoints fewer and farther between, so to speak, you can drift into a new world, a different set of probabilities. The higher and longer you Skip, the farther you may drift from the world you know. That's why you're here instead of there.
"And you can't get back."
A pilot returns and his wife is surprised because he had died in her timeline,
"Well, Glenna? Am I me—the man you married?"
"You can't be." He could barely hear her words. "Woody is dead—I saw him buried." She winced. "Oh, you look like him, talk and act like him—but you can't be him." The gun dropped to the carpet. "I wish to God you could. But you can't." She put her hands to her face—leaning back against the wall she slowly sank to the floor and sat there, sobbing.
in an accident involving a transportation system that seems like pneumatic tubes: a number of vehicles were shot out into unsupported air due to a switching error or something like that.
"Dead, sir?" Pearsall stared at Forgues' blue-tinted image and shook his head. "One of us has to be crazy."
"That's possible," said the admiral. "Why else would you pretend to be a man who was killed more than a year ago? Tube train failure—you must have seen it in the news. The propelling field collapsed; cars smashed out through the girders. At least seventy dead."
Also, he wasn't good to her in her timeline; and in his timeline she was not good to him. They conclude that their bad feelings can be set aside as they each got an “upgrade” in the swap, and a second chance at happiness.
"I mean, come home, Woody! You were right—we're the best Woody and Glenna we can find. Maybe an improvement on the originals—we can try, anyway!"
And, committed couples must pilot as a team from now on. The timeline slippage is slight and doesn't affect global events, so movement of goods and scientific study is only slightly bothered, from the point of view of those who are not the ones travelling.
"The difference between one world and another may be important to individuals, sir, but on the larger scale—politics, economics, commerce—it would be minor, even unnoticeable. Every version of Harper's Touchdown is going to need new counteragents against the cyclic insect mutations, for instance. And—well, draw your own examples, sir—you have more data on the colonies than I do. And communications dealing with overall problems rather than individual ones will still be valid—especially if the first messages explain the multiple world concept, to alert everyone to be on the lookout for discrepancies.
If our thinking is careful, sir, the courier ships can do almost the job they were planned for."
In another adventure, the couple pick up someone with an illness and return to find Earth will not let them land.
Raelle leaned forward. "You can't turn us away like this! We have a sick child aboard. She needs help—now."
Immediately Jay knew they had lost. After the three-second lag the voice said, "Sick? No, thanks—not another Plague. You—"
Overriding the voice, Jay ceased to listen. "Not Plague. It's a metabolic disorder—attacks only young children born on Waterfall. We have the data. Your facilities—"
He waited. Slowly the voice came. "I'm sorry. Even if you're right, we can't take the chance. And neither can you! One thing I hadn't mentioned. All of us—Plague survivors and their descendants—we're carriers. You couldn't come down here and stay alive."
They figure out they can travel between timelines intentionally, using nonstandard settings to enhance the slippage and yet minimize pseudovelocity, and make a quick loop around the moon,
As Skip Factor built—odd, how differently Search resonated to the exciter alone without the thrusters' growl—Jay made small maneuvers, shifting Search's orbit to Lunar ecliptic for the greatest stability he could compute. As he finished that chore he saw Skip pass five thousand—when he ceased drawing power the rate of increase curved upward. And they seemed to race, not coast, around Luna.
and arrive again to an Earth that has no problems with the disease and trivially deals with it.
Now Raelle spoke. "We have a child aboard—" and quickly she told of Areyn's plight. "We've brought a sample of the basic medicine, and all the data available. If you—"
The man shook his head. "We don't have even a start on that kind of problem." Then he must have seen, as Jay saw, how her mouth compressed. For he said, "But we have time, you see. You say you've slowed the little girl's life processes by a factor of four or five—something like that." He smiled. "We can slow them nearly to zero—virtually suspend them, indefinitely—without harm. So bring her—our people will begin work with what you've brought, and sooner or later the child will live."