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In no specific order:
Target Bar: The target bar should be above your own, having to move your eyes up and down across the screen to monitor your opponent and your own mana is a huge strain.
Stats Page: I have to squint to remind myself who I'm fighting against, the icons should be bigger, since the icon art tends to be pretty cluttered it's hard to distinguish between them when they're greyed out.
Minimap: The minimap is too colorful, and the tiny player icons don't really tell me what it should. Either simplify the minimap graphics or include a highlight mode that only displays essential information (unpathable terrain, creeps, towers, players). The current ping icon right now is unnoticeable. Yellow on tan background is not good for alerts.
Item icons: Larger item icons, same problem with the hero icons. I have to squint to see what they are carrying.
Item Shop: Right now it's a pain to navigate it. I heard something about a customizable shopping list to make buying things easier, and would like to see this implemented soon.
Activated Items: There's a distinct lack of activated items beyond consumables. Why not bind the items from 1-6 since your hand is already there anyway? I need my Guinsoo's Scythe of Vyse.
Text Color: Allied chat should be green as it is now, all chat should be white. The red text is hard to see. Same goes for the status page, larger fonts, make it all white or green, it's pretty difficult to confuse your own stats for those of your opponents. Same goes for buddy chat, blue on black is hard to read.
HP bars: Right now it's hard for melee champions on blue side to last-hit early in the game because the champion HP bar overlaps the creep HP bar. Put them closer to the hero's head, give the creep bars precedence and make the creep bars smaller so you know which one is which.
Attack Ground: If there's no plan to let us customize our keybindings then put attack ground as "D", "F", "T", or "G". Preferably "T" or "G" so you don't Flash by mistake.