The highest resolution that the game normally supports is 800x600. Is there anything I can do on Battle.net that's legal that will increase the resolution?
Here's a blue post regarding the resolution:
As of right now we're focusing on compatibility and bug fixing for Diablo II. While a higher resolution would be awesome and on our radar, as of right now it's not top priority.
And another more recent blue post with regards to whether the resolution will ever be increased:
I won't say never but it's unlikely due to how much work it would require on such an older game.
The first blue post also stated:
A Glide Wrapper would not a bannable offense.
So I guess you could use a Glide Wrapper to scale Diablo 2 to your desktop resolution (but it'll still be 800 x 600) to make it run smoother.