One thing I'd love to see from Pokemon Showdown that a lot of other simulators have never messed with is the implementation of Pokeballs. Yes, this seems really minor, but the Pokeball a Pokemon's sent out in can reveal a lot of critical information.
Probably the best example I can give for how crucial seeing what Pokeball a Pokemon's released in is the Crown Beasts. On Wifi, if I see a Shiny Raikou coming out of a cherish ball, I know a lot about it and how to work around it. I know for certain it's Rash and more than likely carrying Aura Sphere. I know that I probably can't switch in much safetly, but I'll have an easier time revenge killing it, at the very least. Likewise, if I see a Raikou in any other ball, I instantly know the threat of Aura Sphere is gone and that it's probably some typical CM variant. However, with every simulator I'm aware of, I can't get that information and I'm stuck in a guessing game I wouldn't have playing on a cartridge.
For other examples, there are things like Crown Entei, Oblivia Heatran, V-Create Rayquaza and Victini, and a host of other events that came with event attacks that conflict with certain other characteristics. This is definitely really, really low priority, but I think this would be a step in the right direction if Showdown wants to call itself the most accurate sim around!