Twitter search is a great feature but it in no way threatens Google's dominance in search.
Recency does not equal relevance
The major flaw of using Twitter as a search engine is that recent tweets on a subject do not equal relevance on that subject. This should be obvious but lets do a few searches to illustrate the point. I'll use searches that appeared in the top 100 from the Google Hot Trends list at some point on February 15, 2009.
Which of the results best satisfies the query? Without question it's Google. Let's try another.
Daytona 500 Pace Car
In this instance both provide the answer. The Daytona 500 Pace Car is a 2010 Chevy Camaro. The Google result tells me it's black and gold and gives me plenty of authority sites to visit.
Twitter on the other hand doesn't provide this level of detail. In addition, two of the five results are from Mahalo and a third is from kinougo. More on 'him' later. For now lets try one last search.
Hands down Google satisfies this query better than Twitter. The only link available is, again, from our friend kinougo. So who is kinougo?
Essentially auto generated Tweets based on hot searches. But where do they lead?
Look at that! An API based link farm with Google AdSense as the revenue source. That looks ... awful!
Twitter would have been a near complete bust if it were not for Mahalo and kinougo. Yet, these sites are simply exploiting Twitter search, not contributing to it in a natural way. I doubt the user experience on these clicks would reinforce the idea that Twitter was the place to search. Probably the exact opposite.
Recency works only for hyper real-time events: earthquakes, Presidential debates and conferences to name a few. (Sidenote: There's this other site called FriendFeed which actually did a bang up job on real-time commentary on the Presidential debates.)
Authority is nonexistent
What makes anyone believe that the latest 5 or 10 tweets on a subject are at all authoritative! Twitter has no mechanism to determine what is the best result for a given query other than the Tweets from their users in a very short time span. Do you trust the random users of Twitter that much? I don't and neither does Google.
The Google algorithm tries to present the most authoritative, the most right, the most useful results, not just johnny-come-lately blog posts and certainly not some 140 character missive. They might not always get it right, but they're trying ... hard.
Duplication is a problem
Twitter doesn't handle duplicate results, opening itself up for SPAM both real and unintentional. Even for the hyper real-time events how many times do you need to see the same quote over and over again?
Twitter is not a Google competitor
Relevance, authority and duplication all ensure that Twitter is not, and likely never will be, a Google competitor. At best Twitter could provide supplemental information to a real search engine. Twitter is the crawl at the bottom of a cable news channel.
"I just ate a mango" isn't going to disrupt the search world.