It is incorrect to put two spaces after a period. Period.
Who says its incorrect? Every modern typographer agrees on the one-space rule. Every modern style guide agrees that there should be one space after a period – The Chicago Manual of Style, the AP Stylebook, and the Modern Language Association all recommend using one space after a period at the end of a sentence.
So, why do so many of us think using two spaces is appropriate? Because of the manual typewriter. Typewriters used monospaced type, meaning that each character occupied an equal amount of space. With monospaced type text looks uneven and there is a lot of white space between some characters so it’s more difficult to spot periods between sentences. Thus, the two-space rule after a period was adopted so that text typed on a typewriter is more readable.
Of course, monospaced fonts, other than courier, are not used anymore. Computers use proportional fonts and electric typewriters from the 1970s on mainly used proportional fonts rather than monospaced.
So, there is no need to use two spaces after a period. It does not enhance readability and there is some evidence that use of two spaces diminishes readability. Think of all the wasted space created by all of us with our extra spaces at the end of a sentence. Imagine what we could do with all the space saved by using just one space rather than two!
Note: for many people, including me, it is hard not to hit the space key twice after typing a sentence. I had to go back and take out a bunch of extra spaces after typing this IFOD!!!!!