One of life's crumpled rose petals has been smoothed out at last! When I formatted my books for e-publishing, they looked perfect on Smashwords and in all other formats but Kindle, and it took me forever to find out why!
The publishing convention for paper books is that the first line of a chapter, or a section after a line-break, is NOT indented, like this.
Then all the other lines are indented, like this!
It looks unprofessional if you don't format your books that way, as if you didn't know any better. But for some bonkers reason, Kindle insists on adding an indent. I didn't want an indent. I'd set the styles function of Word to remove the indent, an indent looked completely and utterly wrong, but, there it was, every time: a rubbish, extra indent.
I rummaged around the Internet. As usual, I didn't keep proper notes, so I can't credit anyone, but thanks to all those helpful posters, and eventually, I pieced together what I needed to know. Here is my (nontechnical) version in case it helps anyone else.
Those extra indents appear because Kindle is trying to be helpful - seems a lot of folk try to upload manuscripts with no paragraphing, so Kindle has been set to add a paragraph space automatically, but whoever wrote the programme didn't add the publisher's beginning-of-a-chapter-has-no-indent option. You have not gone crazy or formatted wrong. Kindle is overriding your instructions.
The way to fool Kindle is to go into the styles section of Word and alter your first line style. (If this means nothing to you, then I recommend the FREE styles guide over at Smashwords by Mark Coker.) If you right click it allows you to 'modify' then you select paragraph, then, where it gives you the option to set an indent, you set the tiniest possible indent 00.1 cm will do it. It is invisible to the naked eye, but it makes Kindle happy because it reads that line as having a proper indent. Your text looks professional. Everybody is happy. Hurrah!