what thing do you think riot could improve that would go the furthest to creating a situation where the community trusts riot again?

I think there are 3 things.
1) We need to just talk more and earlier. When we maintain radio silence, players fill in the gaps with their own speculations, which are sometimes correct and many times not. I think we've struggled here to find the right balance, because if we talk about a problem too early with no solution immediately in sight, then it can feel to players like we are ridiculously slow or lack a sense of urgency. I recently mentioned that we want to update runes, but it's not going to be in the next several months. We will see how that goes over. :)
2) Second, we need to shift our tone a little. The "brand" for Riot (though I kind of hate using that word) has always been the scrappy start-up that does things differently. When we were a little sloppy or brash or unconventional, it fit that narrative. But we aren't really that company any longer, and we need to figure out a new way to have a conversation that keeps our company culture intact but evolves to reflect the reality of the current size of Riot and success of LoL.
3) We need to deliver good shit. Talking about our philosophies and future plans can help a lot to fill in dry periods, but if all we ever produce is talk, then players will understandably lose faith. This has been a bit of a slow year from us product-wise, because so much energy has gone into the client update, an we burned some player trust with the loss of solo queue.
Great question and one we discuss a lot.