Matt Cutts and other prominent Google folk recently held a live Q&A session, aimed at addressing important questions from Web professionals. The full discourse is extensive. What follows are some points of interest, including dedciated vs. shared IPs, article directories and 301 redirects. You can see the entire conversation here. I think what's important to look for, aside from concrete answers, is the tone of the answers. That can give you a good idea of how Google feels "behind the scenes."
Does getting a lot of comments in a blog help in being well indexed/ranked by Google?
Having a lot of enthusiastic users commenting on your posts and doing so generating content on your site, certainly does not harm your rankings :-) Furthermore, a large fan base gives the webmaster a bit of independence from search engine traffic, which is the reason why generating original and compelling content in order to nurture a group of committed users is something I would highly recommend to any blogger.
How often does your search algorithm change?
We change the algorithms all the time - last year we had over 450 changes.
What weightage is given to the links from social networking sites and blogs?
I would treat social sites and blogs the same as any other site.
Are .gov and .edu back links still considered more "link juice" than the common back link?
This is a common misconception--you don't get any PageRank boost from having an .edu link or .gov link automatically. Hah John, I beat you to it! If you get an .edu link and no one is linking to that .edu page, you're not going to get any PageRank at all because that .edu page doesn't have any PageRank.
JohnMu: We generally treat all links the same - be it from .gov or .edu or .info sites.
Have links from article sites been de-valued at all?
In my experience, not every article directory site is high-quality. Sometimes you see a ton of articles copied all over the place, and it's hard to even find original content on the site. The user experience for a lot of those article directory sites can be pretty bad too. So you'd see users landing on those sorts of pages have a bad experience.
If you're thinking of boosting your reputation and getting to be well-known, I might not start as the very first thing with an article directory. Sometimes it's nice to get to be known a little better before jumping in and submitting a ton of articles as the first thing.
Does 301 Redirect move the Google Page Ranking to the new location? If so how long does it take for this to take effect?
Where appropriate, ranking signals will be transferred across 301 redirects (if the same page has moved from one URL to another). This may take some time, so you should probably leave the redirect in place as long as you have control over the URL. That way any new links will make our crawler follow the 301.
Will it make any difference between a shared IP and a dedicated IP on SEO or search results, as opinions are divided on this aspect?
Most of the web is on shared IP addresses, so it doesn't make much sense for us to give those on dedicated IP addresses any advantages. That said, if your server is struggling with the load of your website, it might make sense to move to a dedicated server that helps to make sure that your users are happy when visiting your website.