Q:

Do "Advanced Super Ninja Search Options" work correctly with regards to spaces? 

As I understand it, searching for title: "halting problem should return only questions with the quoted string in the title.   However, that is not the case, and indeed those results are the same as searching for "halting problem". 
It appears that I need to remove the space after "title:" in order to get the desired results: title:"halting problem".   That the space made the "title:" portion useless was surprising to me.   Furthermore, the Search Options page indicates that "title:" and "body:" operate on all following terms.   That doesn't seem to be happening here. 

A:

The old search help with an inaccurate description here has been removed.   All advanced search options do not need a space after the colon...doing so will make them not work. 
Additionally, we now show any advanced options on the right so you can see exactly what happened when we parsed your search request.