Some things I'd like to see:
I'd like to have access to the item store during the game, just so I can see the stats on all items, not just the ones that have been built.
Also, flags on the timeline for important events like Baron, Dragon and tower kills, First Blood, and multikills (and maybe times when there are a burst of kills in a short span of time? I'm not sure if that's possible, but something to indicate teamfights is the general idea) would be useful for rewinding to find exciting gameplay moments.
An option where, for example, the champion you have double-clicked can display some sort of indicator above their health bar every time they use an ability, like the ability icon plus the hotkey or something. The idea being that if you want to get an idea of the order someone used their skills during a hectic teamfight where the audio and visual cues can be difficult to see.