Previously, I wrote an article about How to Improve Google. I also wrote about how to build a search engine to compete with Google. I had a number of criticisms of Google but as I read somewhere "Google may let people stuff the ballot boxes but at least it allows people to vote" and "Bing is a decision engine but it decides for you."
Bing is not a better search engine than Google because it isn't trying to be. It's trying to compete with Google only in money making traffic. Using Facebook likes to help determine search results isn't a step in the right direction.
Bing is horrible at indexing new websites. If you want to find your friends website, use Google. If you want to shop use bing. If you look at Bing and look right over next to the web tab, you can see a shopping tab. Google hides it's shopping tab better.
Bing is not a search engine. It's not designed to find sites. If you're looking for obscure information, Bing won't help you find it. What Bing is good at is helping people to shop online and find the best prices. Bing is a shopping engine.
The first way to improve Bing is to improve it's marketing. Decision Engine still implied that it was a search engine and could you find what you were looking for. Bing is good for mainstream and pop culture stuff. Naming it as a pop culture engine would be good for marketing as that would imply shopping as well.
Then people will know that you have to bend over backwards to get indexed with Bing and if you're looking for information about your buddy's latest blog post you should use google. If Bing was marketed as a pop culture engine then people would know that they should use it to find Access Hollywoods page on Katie Perry but they shouldn't expect to find Joe Nobodies(sucks for us Joe Nobodies though)...
Bing is very bad for smaller publishers but very good for internet noobs who don't want to see spam(an advantage of not indexing anything). Bing isn't the ideal website that internet publishers would like to see to compete with Google(one with less reliance on backlinks and more on content) but it's one way to target a particular branch of Google's market.
Bing should only try to compete with Google in one area: buying traffic. Integrating facebook likes doesn't help with that. Buying traffic is swayed by ads and product placement. The best way to improve the Bing search engine for this kind of traffic is to provide the best deals and to show the most shopping options.
If Bing goes after all the shopping traffic then it'll force Google to improve it's algorithm for information traffic. Probably a good thing for us publishers.