Ok, #1: Stability. In game, various amounts of client stutter, or connection lag, can absolutely make or break games. I'm on an i7-920, 12gb ram, and GTX 560 TI 448 core. I should have no problems running this game, but there are mysteriously a hair-pulling amount of stutter, slowdown, or other, issues that crop at random. Not trying to draw comparisons, but Dota2 does not do this. Skyrim run awesome. BF3 runs awesome, and Crysis 2 with the DX11 patch and some mods runs at near 60 fps. League shouldn't have these issues. It runs on freaking TI calculators practically, and fairly well, but I'm just mystified at these issues. Note, these also seem to be more pronounced when running mumble, but I've had them without mumble, and it happens on fresh windows installs as well. I can't reproduce them with any consistency, and I'm on all new hardware.
2: The Client/Front End. There are many things that couple be accomplished here, but I'm going to have to come out and say that this AIR front end isn't cutting it. Having to launch a separate executable has many negative impacts on the experience, in my opinion. For instance, things could be pre-loaded while browsing the menus. Like, when you start looking for an SR match, summoner's rift could immediately start loading in the background. During champion select, as each person locks in a champ, that champ data could be pre-loaded. As someone said earlier in the thread, time doesn't grow on trees, and the amount of waiting involved with getting into an average draft game can be up to 10% of actual match time. Loading is just one of the things, there are certainly other advantages to be had.
3: I said it earlier, but High end graphics scaling would be nice. Once again, I don't want to point to the competition, but Dota 2 is doing a very good job here. The art style is a matter of taste, and I prefer league's, but would love to see the next evolution of it.