So, I played a few games, and a lot of my problems were due to the HUD being new, but I identified two major flaws and one way to improve otherwise:
1. I really don't like the OOM icons and the not-able-to-cast icons. I think that the icons should just grey out, since when they change, they draw the eye down, away from where it should be. I also miss the old HUD's way of doing the cooldown countdown, the circular overlay is slightly distracting.
2. I feel like the left bottom corner was an excellent place to have the champion info (AD, AP, MRes etc) and having all the info in the right bottom corner feels off-balance. I also think that a lot of the champion info on AD etc should be permanently visible, so perhaps have AD, AP, Armor and MRes permanently visible in the bottom left and have that expand when the player presses C?
3. COLOR CODING. I was having trouble finding my AS and other stats, when I came up with an awesome idea: color code the values! Damage that comes from AD ratios shows as orange in ability descriptions, so how about displaying the player's AD in the same color? It would help with navigating the character info and would make things easier for newbies.