There are two parameters that aren't documented in the developer API but are used on their Advanced Search page: http://search.twitter.com/advanced
They are ors and ands; which you can use to query more efficiently. At one time they documented that you could take the queries from search.twitter.com and use them with .json like the API. Not sure if that's the case or not.
I also added the filters:link, which has a side effect of limiting the query to only 7 days.
Added a few parameters that aren't documented but are in the search i…
Well... skip this, the only important part is the filter:links, the ors and ands are removed and you can do it by saying...
word1 word2 word3 OR word4 OR word5
and accomplish the same thing