I just started playing about a month ago, and I have to say that the spectator mode has been fantastic! I love being able to watch players to learn new stuff, and I generally just like watching people play. Here are thoughts from the perspective from a newbie:
General
Well this worked as I assumed it would, so I can't say much here. Just some general things: it would be nice if there were downloadable replays, as the ones I've found (leaguereplays) are a pain to watch in comparison to spectating. I guess that's just a good compliment to you guys.
One thing I liked from watching Starcraft 2 replays was that we could see the game from players' point of view. I really liked using this because it shows exactly how a player is looking at things. I'm fairly certain this wouldn't work in a spectate mode, but possibly in a replay mode.
Directed Camera
It took me only a few minutes to figure this out, but I've generally avoided it, because I prefer to watch specific champions. When it's on, I feel that it does a pretty good job of finding fights and keeping them within view, and is generally very smooth. For a completely AI camera, I'm rather impressed.
One thing that I've noticed that is somewhat annoying (but not a huge deal), is that if I follow a champion that dies, and the camera goes to directed, then the champion comes back, the camera stays on directed mode. I would prefer it to go back to the champion that I had been focusing on, but again, this is just nitpicking.
Camera switching wasn't very intuitive until I took the 5 seconds of looking at the keybinds, and now I am very comfortable with it.
Featured Games
If I had any major complaints, they would be in this area. Some things I'd like to see:
Let us see players' ratings easily. I just found out recently that the first games are generally higher rating (or I think I found that out, I'm not actually 100% sure if that's the case), but there is no way of knowing that just by looking at the screens. Currently, the only way to see rating that I've found is to search for a player and look at their ratings, which means I have to switch pages and, occasionally, have the spectate rotation change out while I'm looking at a rating.
Maybe let us search for games by champion. I generally like to watch people that are playing champions I like, and with the current setup I have to just hope there is someone playing one of those champions.
In fact, I would also like searching by player name. I don't think the really good high-level players want to get random invites from me because I want to watch their games, but I still do like to watch them, and currently again just have to hope I'm on when they're on, and that I catch one of their games while they're featured.
Other than that, maybe just some more games up at a time, and make it more obvious when a game is dominion (the graphic change is very dim and easy to miss), and maybe a setting to let us filter out ranked, normal, or dominion games.
Drop-In (off your Friend List)
I've only done this a few times, but it has worked every time, so I can't complain. If anything maybe a clickable button (like clicking on the eye image) that let's us enter a game without having to right-click. But really, I have no actual complaints, and that is a very minor thing.
Spectator HUD
I like the HUD a lot. I have no real complaints, but I did have to spend a little bit of time going through the keybinds because I'd sometimes close out a piece of the HUD by accident and not know how to get it back up.
The timeshift thing is very cool, but one thing I've noticed a few times is that the game would not let me get to "Live," it would force me to 30 seconds behind Live. If I sped up to get to Live, the game would stop (like if I were lagging out or something), and start again when it was back to 30 seconds behind.
BUGS!
Almost every time I spectate, upon entering the game there is a bug where the bottom-right corner of the screen is treated as the top-left corner of the game, so the scrolling is really bizarre. I fix this by alt-tabbing out and in, so it's not a big deal, but it is a bug.
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So yeah, that's what I have to say, as someone that just started and doesn't really know how things work yet. Sorry for typing so much, but I hope it helps.