It looks like standard browsers support few image formats, it’s not that many of them.
Jpeg
GIF
PNG
Saving in Jpeg format seems to be OK,
GIF is trickier, because GIF is compresses by limiting number of colors, and selecting how many of those colors to use, which ones to use and selecting a transparency color is essential for web work.
Next, PNG actually has two modes, unlimited color space and fixed palette, just like GIF. So there should be distinction for those.
Is this something in the plans or is there a work around?
That’s odd- I wonder if PS doesn’t support certain types of PNG files. Can you send us the problem file to support@flyingmeat.com so we can take a look at it?