This may be due to the template I'm using, or maybe even my browser, but in case other people are having the same problem, I thought I'd post my workaround. (Besides, it gives me a handy reference when I forget what to do!)
When I insert images into my blog posts I get a gray border around them. Like this:
NOTE: The border doesn't show up while composing, or in preview, only (annoyingly) after you publish.
To remove it, I edit the HTML and add style="border: none;" to the img tag. (I'm not sure why this is necessary because it already has border="0" - maybe something in the CSS.) The result should be the image without the gray border, like this: