Double-spacing after a period. Like this. Is wrong. But so many people have so many different opinions about double-spacing and single-spacing after punctuation, it's difficult to point to just one reason why it's wrong. I'm going to try anyway.
Single and Fabulous?
The number of spaces that should be placed after a period is actually a hot point of contention among writers, editors and typographers. This is the kind of stuff that gets word nerds all kinds of hot and bothered, and I guess I'm no exception. I passionately believe that only one space should be used following any sentence, and the general school of typography agrees with me.
Typesetters are the people who actually put the words on the page. They're responsible for making everything fit together and using all the space they've got in an economical fashion. Since the early 20th century, it's been an industry standard in Europe and the Americas to use a single space, not a double, between the period and the new sentence.
Standards were much looser before the 19th century, and in the early days of printing typesetters often used enlarged spaces following their periods. But a 19th-century invention would screw all the spacing up and confuse writers even 200 years later.
Ironically, it was the manual typewriter that changed spacing forevermore. The standard space on the manual typewriter was considered by many to be too small to properly separate sentences. Many writers began hitting the spacebar twice, not just once, after every period in order to provide the necessary separation. It became the norm to do this, and double-spaced typing was even taught in typing classes. No one uses manual typewriters anymore, but the error is still being repeated all the time.
If it's an error. The debate continues to rage on to this day, with many hotly defending the usefulness of the double space. I hate it, and I advise against using it, and I'm going to tell you why.
The Way It Is
Typesetters and printers established the single-space standard for a pretty important reason: money. When words take up less space, fewer pages may be used to print out a whole book. Fewer pages equals less cost to make the books, and that means they can be priced more competitively.
It's something no indie author can ignore. CreateSpace is easy and affordable, but it ain't free. Self-published authors can't afford to be less cost-conscious than those huge publishing houses.
It's also important for indies to conform to all industry standards in matters of grammar, punctuation and spacing -- both to fit in with all the other books and to prove that they can. Indies have a bad reputation as being amateurs and hacks, so don't visually separate your books from the ones the big box publishers are churning out by the million.
And because it is a standard, you could get called on it if you do it incorrectly and use a double space. If you do any guest posts or freelance writing assignments, you could easily draw the ire of a blog owner or editor who has very strong opinions. Conform to the standard; they'll definitely let you know if they want you make changes. If they do, just use your search-and-replace function to fix your spacing.