I have found that a given name search has opened doors when the surname has been badly spelled.
Really common names provide one challenge, but rare names provide another. No one knows how to spell them. The surname of my Forsbury family has been spelled many ways. I made a huge breakthough by doing a first name search in the 1851 census for every George born in Hendon, Middlesex, England in 1841 +/- 1 year. Since this is the greater London area, it was a long list. I found the family and it gave their years and places of birth. A Google search found a query from Australia looking for information on George's brother. Within hours I had a reply from a distant cousin, and we both caught up on 150 years of family history!
More recently, I was looking for a Ritson family. I knew that name was Ritson because I had a digital copy of the marriage certificate. The relative asking about them gave me the names and ages of the children, and also spelled the name as Ritson. The problem was that the Ritson family seemed to disappear after the marriage. Ancestry.com has a search engine where you can put in the given names of family members when you do a given name search. It immediately found the family in the 1901 and 1911 UK censuses as Kitson! This is a vast improvement over the old given name searches! It took only seconds instead of hours of searching. I really hope that FamilySearch.org will add this feature to its search engine.
In another case I had a family where some members changed their surname. A first name search made it easier to find them regardless which surname they were using at the time.