The One Question…
Our search firm is doing a good job generating flow for our open need.  They seem prepared on questions related to compensation, red flags in a candidate’s background, availability, etc.  Are there any questions you think we should ask our search professional about candidates?
Part of the reason you are using a search firm is to have them ask the difficult candidate questions.  I spend a lot of time early on with candidates asking them about their motivation for changing jobs, their successes, their failures and their relationships with key stakeholders.  I want to be prepared for any question a client might ask.
The one question I rarely get nowadays from clients is “how would I rate the candidate?” It’s surprising that more clients don’t ask this question as it forces search professionals to provide more data on candidate likes and dislikes.  The risk to the search firm is that if they are too positive in their assessment, they might lose credibility if the candidate doesn’t interview well.  If the search firm is not overly positive on a candidate, the firm runs the risk of the candidate not being interviewed.  
In my opinion, I feel an open and honest exchange with clients helps strengthens the relationship as well as alignment on the candidate profile.  Ultimately I want to be the eyes and ears for my client and think about talent the way that they do.  So every exchange, however painful, is a valuable one for me.
My sense is that clients don’t ask search firms to rate candidates because the reply may focus on all the positives without much commentary on concerns or risks.  If this is a legitimate concern, clients could ask the search firms different questions that help tease out feedback on the candidates:
What do believe will limit this individual’s growth within our company?
What percentile would you put this person in relative to his/her peers?
How would you force rank this candidate against all the others you have considered or presented for the role?
If a client asks their search partner for candidate ratings, the longer term outcome could be that the client and search partner are lockstep in assessing what “great” looks like.