With a hold on the search market share like Google has, how would you imagine a company becoming the next search engine giant?
DuckDuckGo, a small company, has been trying but wasn't able to.
Bing, with millions invested by Microsoft, has been trying but hasn't been able to.
If you were tasked with this, what areas would you say are Google's weak points?
If somebody kidnapped my family and forced me to start a business in the search market or never see them again, I don't think I'd attempt to take Google head on.
Google does search in the general case incredibly well. While I can think of some features I'd add, or tweaks I'd make, the moment I built anything that could threaten Google in any significant capacity, they'd take those new features and quickly implement them as well.
No, I think if I had to get into the search arena, I'd be looking to carve out niche markets, not go head to head. Google search is great in the general case, but for specific niche areas, the general solution isn't nearly as good as what you could do with a specific tailor-made search for the niche.
An example of this that comes to my mind is wolframalpha.com, which is very number oriented. It's a specific niche, and not everyone will find it useful. Definitely, it won't work for all things. But compare the results that Google, Bing, and Wolfram Alpha return for the query "Is the population of Canada more than the population of California?"
Wolfram Alpha actually gives an answer and (sort of) explains how it got there. Google and Bing give you a pile of results that you still have to sort through, and it's hard to know how authoritative most of them are.
This may not be exactly what you're looking for, because this wouldn't actually take down Google. It could be, however, a reasonable pathway into the search area, which depending on your the interpretation of the initial question is may be good enough.
Google's weakest point isn't their search, it's their dominance. I'm fairly sure they'd love some half decent competition right now - if only to prevent their trade marked name entering natural language at which point, they won't be able to defend it as rigorously as they would like.
The reason no-one else has done as well as Google with something as "simple" as search? Most people don't need anything that Google doesn't already do well. It's fast, it's accurate and it's free.
I would say that "search", the problem, has been fairly well solved. The problem with every company that has tried to compete with Google on search is that they are trying to have more relevant search results. Going from 90% relevant to 95% isn't going to sway users away from Google -- because users perceive Google as being the authority on search.
DuckDuckGo has carved a small niche for itself by being the search engine for people who value privacy. It's a great effort by Gabriel Weinberg.
I'd say Facebook has the best chance at the moment to take the search crown away from Google. With the amount of data they have on users, creating a search engine that factors in the social graph could do it.
In terms of weaknesses, Google's biggest weakness is that 85% of it's revenue comes from ads. That might be one way to take a stab at the beast.