To put it in context and a bit of background, I usually play random battles only.
When downloading a replay as a html file, Pokemon team, stats, abilites, EVs, IVs and movesets etc should also be downloaded. It's relatively small sized data but really relevant. This way, one can figure out what went wrong and stuff.
When you try and see the opponent's Pokemon (hover the mouse over it), only the min-max speed is visible. Other min-max stats should be visible too.
Random battles should have separate tiers too. Example, random OU should ban Blaziken, etc. Or at least give both players Pokemon of generally equal power.
Lastly, Thanks, guys, you do an awesome job with PS. It got me back into Pokemon after a long time of inactivity.