Basically, the issue is, when you enable 'hardware graphics mode' in byond's settings and allow byond to use your GPU to display the graphics, stretching the image by using the '64x64' mode or the 'stretch to fit' mode, the game looks like a blurry fucking mess.
This is because some graphics cards simply scale sprites in this blurry fashion, instead of using nearest neighbor scaling which looks sharp and great.
Here are some examples:
In my case, all you have to do is right click or open one of the top program menus and the game suddenly becomes sharp, as evidenced by the first two screenshots. This is bizarre as fuck, but the game should ALWAYS look sharp like this. I don't know why byond (or ss13) defaults to being blurry like this, and I've tried every graphics option under the sun.