I am really liking the fact that this part has worked so well in my games. If someone says "hey, I made a mistake. Can I go back and do X?" everyone has let them do that.
In a private game to show my wife the ropes of the video game and how it works and where buttons are, I went back and did an Argent Adept turn differently five times in a row. She was less enthused.
I reminded her it was my way of teaching her how to hit the Rewind!
I try to only give advice when there is something that the player could have done that was strictly better than what they did do. Even then, if the difference is a few hp or something else minor (like a Summon Staff), then I might not mention it because it's not worth the hassle to rewind.
For example, AA using the Lyre + Supertonic to get an extra Inventive Preparation before using their main power usage. Strictly better, and very useful.
If there's a significant pause on a turn I will suggest a card/power (via the ultra annoying beep), I don't think that's alpha gamer mentality.
And occassionaly I will ask/suggest things in chat on how to handle a particularly deadly situation we are in but suggesting a move is not the same thing as controlling a player's action.
I have seen lots of "sub-optimal" plays (Why would you play a Legacy Ring against Dawn when you have 3 other good cards in hand and no extras powers, not even on the cards in hand?!) since the multiplayer started up (and none that I can remember in real world play, although I'm sure there were) and while I might silently seethe on the other side of my computer I have not expressed this in game.
EDIT: Also, isn't suggesting things to other players a way of teaching an intricacy of the game that they might have previously missed? (I taught someone the Prejudice, Pride, Prejudice combo on the app recently).
I made two suggestions to the Trello board about this:
1) Have in the config (so you can turn on and off) a delay to suggestions. This way someone doesn't instantly tell someone what to do, and you have a chance to look around at what's what.
2) A "help me" button where you are telling everyone that you want suggestion for this play.
The idea about a "help me" button is really nice.
I like both of these suggestions a lot.
Had a player the other day play Infrared Eyepiece directly when they had Impromptu Invention in their hand. Guess they just didn't think about it!
I third this idea! the 'help me' button would be especially nice for me when I'm playing aa and I want everyone's opinions on what they'd like done.
Clicking the "help me" button could also reveal your cards to all the other players, for that turn, so they can know what the options are.
Another suggestion that I submitted: In order to minimize the use the of the chat box, have a list of suggestions that go on the main board that are always seen, and are shown when you have to make a choice. For example, you can select a particluar card in play and put on: "destroy first", "I can take this out", "don't destroy", etc.
So, I learned that you should never play Matriarch on multiplayer.
Matriarch is bad enough when one person has to click through everything. When you have to depend on multiple people (and possibly the communication lag), it takes forever.
We had about a dozen birds get wiped out with a Carrion Fields and Stealth Bot out. Fortunately Heroic Interception meant that only Legacy's damage prompted a Stealth Bot question, or I'd still be in that game wading through check boxes.
I found the suggestion thing kind of annoying in the couple of games I've played on Steam - if I was at tabletop I wouldn't be telling people which cards I think they should play, and I wouldn't expect anyone to do the same to me. I just tried to ignore the numbers when they poped up (once someone actually explained what they were, lol). Harder to ignore was the fact that my cards kept glowing/flashing in a "Hey! You need to click one of these now!" kind of way which I just found distracting and irritating. It would also have been nice if the chast was visible without it needing to be in a pop-up thingy, but with a screen that busy I suppose there's no room so I can understand that ;).
It might be a bit sort of clunky but generally I can get past that to play with forum people and stuff - only had a couple of games so far, a few days ago with some people :).
After playing the digital version so much I don't even notice the card glow any more. And it sounds like you'd probably work better in a not 'open hand' game, which is the setting that let's everyone see what cards you have.
And I think I may have been that person who explained the numbers to you. I was in your first multiplayer game, if I'm not mistaken, and you didn't know what they were if I remember correctly. 
Yeah probably, I haven't played since (well, I tried yesterday but it bugged out and then I had to go anyway) so that would've been you :). I don't mind being able to see people's cards - it's handy if I'm playing a hero who can let other players do stuff, so I can decide whom to give those kinds of bonuses to. And if I'm playing at tabletop we have our hands just laid out on the table. When the vote thingys come up in the Steam version I just generally try to ignore them. It would be nice if they could be toggled off, though - I get being able to vote on stuff that affects everyone (eg deciding which target gets hit first in a multi-hit attack in case that target can retaliate in some way and stop everyone else taking damage or whatever), but on a player's turn? Nah, I'll ask in chat if I need suggestions. I'd much rather do that than have a bunch of impersonal, emotionless numbers come up on my screen ;).
And I prefer the speed of a number that says "maybe hit this guy" so I can think oh yeah that works, rather than choosing something else and then getting a chat message saying to hit that guy and then rewinding.
I like the number showing up from suggestions as it is quicker than chat. And if you really question it the you can go to chat about it.
I like the number but would like a delay on people being able to vote on other player's turns.
I don't need you to suggest every. single. CARD PLAY. 
PLAY ZEALOUS OFFENSE!
I'm among those that don't need suggestions every time, but there are plenty of situations where I want input from my fellow players(Like when I want to know what things everyone needs when I start getting crazy with AA). So a merger between both voting and chat works out for me perfectly.
I just don't need anyone telling me 'how' to play, thank you. :/