Matters zero for desktop browsers. They all render in 8 bit truecolor these days. if at all, it may be an issue for mobile devices, but those, too, usualyl are based on the same browser code and will handle any color conversions and dithering dynamically based on their drawing APIs.
Thank you so much Mylenium!!
sorry so long to get back to this question but i had to send my laptop to the doctor for a while.
I'm not sure I agree Mylenium. I did find it made it a visible-to-the-eye difference on my desktop browser today.
Had a logo, saving it to png 24, original Illustrator file 580 px wide, using save for web function, 380px wide export.... clicking the box made a significant difference in the resulting crispness of the logo when imported into Muse at 100%, and then rendered in desktop browser.
This is on my iMac that is NOT Retina display.
Facebook was destroying the profile image (simple 2 color logo on white), no matter if it was in jpeg or png, it looked VERY low quality. Checking Browser Dither solved the problem. So: if fb gives you trouble, check it.