I have two neat picks here, that caused my opinion to lean towards SO absence of too trivial downvoting.
First is, community would miss a very present hostile mechanism against "unwanted" behaviour, what would cause the community to be actually more friendly and trusting (it is like carrying a gun saying we need friendly community).
Yes, that is one of the downsides. You become used to it, but it could potentially drive away new users before they become established here.
Secondly, SO has resulted in a very effective voting system, where solid answers earn 10+ up rates, majestic answers earn 30+ rates, while missleading answers dwell with 0s, and not very targeted answers earn few points if still providing an interesting offtopic fact.
No, misleading answers get upvotes because they seem helpful. People correct the answers in the comments, the answerer updates his answer often without crediting the sources, and continues to get upvoted, so it incentizes the fastest answers, and the most correct looking answers, and the people providing the real insight in the comments (i.e. "You're wrong here, it's X not Y") don't get rating boosts. Their comments get upvoted, but the upvotes don't contribute reputation. Often times on GameDev.net, the real value comes out of the discussion of why someone's answer is actually wrong.
My only suggestion to improve down voting, that I am a little concerned about, is that down vote would be penaltized by -3 points,
The person being voted down gets -3, the person doing the down-voting gets -1. i.e. it costs 1 point to penalize someone 3 points.
what would then become a privilege of only very core members of community,
No, even if you have zero reputation, you can still downvote. Your score just goes into the negative.
so they could target the missinformative and incorrect statements,
A few do that. But most long-standing members of the community don't target misinformation and incorrect statements with voting. We target it by replying to it with correct info.
Often times, if someone says something incorrect but in a friendly and helpful way, I upvote them for their helpfulness while replying to argue against their faulty knowledge.
way for more free discussions, where the right point oposition will have to make clear reasoning even to less informed observers of the thread.
This is what we often get already. You'd be incredibly hard-pressed to find a negative voted post that has not been replied to by one or members of the community.
In the lounge, downvoting and upvoting is disabled entirely, because people were using them too much to say "I agree with your personal political viewpoint", or "I disagree with your views". But they are intentionally in existence for the technical forums because we want to upvote the helpful posters, downvote the rude posters.
Yes, some people upvote for helpful information, which is fine, and others downvote for incorrect information, which I disagree with. But overall, it seems to be working. I don't see people afraid to post dissenting views because of fear of downvoting - and I do see dissenting views and discussions, where the people arguing against each other keep upvoting each others' posts.
Even with absence of negative voting, SO has still became a provider of knowledge bonity in the pro-sphere to its members of large reputation.
If you are talking about the reputation bounty:
Higher reputation users can give a huge chunk of reputation to people who haven't earned it normally, just because that person has quickly provided some answer the higher rep person needed. How is that fair that the person getting the rep got it without earning it normally?
Don't you think the idea that high reputation users can get quicker answers to their problems unfair? What, is a higher rep user's questions more important than a newbie's question?
Gamedev surely needs to change something to become more attractive
Why do we need to be more "attractive"? Ideally we'd have a large, stable, knowledgeable, and helpful/friendly community.
(By 'stable' I mean you regularly see the same users, so can develop semi-relationships with individuals)
Gamedev is Stable (or perhaps even shrinking), Knowledable, and Helpful/Friendly. It's lacking in largeness; it'd be good if the community would grow, but I don't think the reputation system is what's holding back growth. I think the number of people who want discussion is smaller than the group of people who want a McDonalds answer in 5 minutes or less (which often is all I'm looking for as well); but I don't want to just assume this is true, or it might become some kind of cop-out to resist change. I'm open to change if it improves things (though I may kick and scream for the first few weeks 
), but I don't believe all change is automatically good just because it's different.
Stack Overflow is large, it's hard to see if it's stable. Some users stay around, some come and go.
Stack Overflow rewards fast knowledge, some of the users are genuinely knowledgeable, many just regurgitate answers they heard from others without understanding it, and often give the right answers to the wrong situations, and are rewarded because it looks correct.
As far as friendliness, Stack Overflow is hit and miss. You get some friendly users, and then you get bureaucratic robo-users that get a taste of power and start acting like jerks, and are incentived to do that. Have you never noticed this? Long-time Stack Overflow users have a serious attitude problem, where it feels like you're almost on the phone with an AT&T "customer representative". It makes me want to reply with, "Oh, I'm so sorry I stepped in your little fiefdom. Say hello to Comrade Stalin next time you see him.". Most often I'm just observing this interaction between other users (often times months or years in the past, when I'm googling for a McAnswer to a question I have), and am not actually involved myself.
We have a few users who are jerky in their responses, despite being incredibly helpful, but they are very few. Most of the community is highly helpful and highly knowledgeable. Stack Overflow has a smaller ratio on both those areas.
Stack Overflow just hands out points like cookies, I log into the site and questions I answered months ago are still rewarding me, it's just "feel good" addiction-based extrinsic motivators. It does feel good. But just because something "feels" good that doesn't make it actually good or beneficial to me or the community long-term.
But ofcourse, Stack Overflow does gets points for "a succinct paragraph answer right when you need it", and GameDev.net gets points for "intelligent discussions going deep into the ramifications and reasons why a particular answer is good, and what the alternatives are".
There's a place for Stack Overflow microwavable answers, and there's a place for real five-course discussion. Different formats. The different reputation systems are even focused on entirely different goals: Stack Overflow rewards active/frequent participation regardless of quality (and also rewards bureaucracy - which is bad, and administration - which is good), GameDev.net rewards participation but especially rewards friendly knowledgeable discussion.
