Would it make sense to have someone write separate teaching and non-teaching letters of reference for one candidate? There's a friend of mine (seriously, not me) who is facing a slight dilemma.  There's a particular senior mathematician who he knows well (several co-authored papers, etc.) who also is probably the person best placed to comment on his teaching abilities.  Now, of course, this sounds very convenient; after all you can roll lots of praise into one letter, right?
But there's an issue with this: I know for a fact that many people on search committees don't read the letters that are supposed to concern teaching.  Certainly, many will not to read them until one has gotten down to a fairly short list.  So you don't necessarily want lots of praise for your accomplishments in general to be in a letter which has "(teaching)" next to it on MathJobs.  I'm trying to think of what to suggest to my friend as a way out of this dilemma, and one idea which floated to the top of my mind was this:  maybe this senior person could write two separate letters, one for teaching and one for everything else.  Is this an insane idea?  Is there some better way out of this dilemma?
 A: This is a reasonable thing to do, and is definitely possible in mathjobs--indeed, I believe that we have just offered a job to an individual whose mathjobs-based application had distinct research and teaching letters from the same person.  He also had a teaching letter from someone else, as well as a surplus of research letters, consistently with Pete's advice.  
I'm not sure how this worked on the letter-writer's end, but on our end the only difference is that there are two files next to the letter-writer's name rather than the usual one.  The modifier "(teaching)" which usually appears next to the name of the authors of teaching letters, does not appear next to the name of the letter-writer in question--though maybe this is only because it is quite generally the case that you're only allowed to specify one person as your teaching reference,* and the applicant would have specified the author of the other teaching letter.  
*I don't remember whether this is true, but looking at other applications with two teaching letters suggests that it is.
A: Dear Ben,
Yes, it is reasonable to write a separate teaching and research letter, for exactly the reasons you write above: application readers often separate the teaching and research letters in their minds and (at research institutions) they may not give much attention to the former letter.  (Although if the teaching letter is written by a sufficiently famous mathematician who is an obvious leader in the applicant's field, I think the danger of this is much reduced.)  Note also that recommendation letter inflation being what it is, many sharp-eyed readers will snap at almost anything as a sign of lack of strength.  Talking about the candidate's teaching when you are supposed to be (in the eyes of the reader) talking about their research will definitely be taken by many readers as a sign of research weakness. 
On the other hand, if I ask for four letters -- three research and one teaching -- and your application gives me four letters, but two written by the same person, it is natural for me to feel a little cheated.  Surely part of my request was to get opinions from four different people?
So here's what I will recommend: if one person has serious things to say about the person's research and their teaching, s/he should write separate letters (and briefly explain this in both of the letters).  However, at the same time one more letter should be included in the application: i.e., all together, one teaching letter from Professor A, one research letter from Professor A, and three more research letters from Professors X, Y and Z.  Note that one of X,Y,Z should probably be the student's thesis advisor (in particular, the advisor should not be Professor A).
I have never seen this arrangement in an application, but I can find nothing objectionable about it.  Indeed it would look to me like the candidate had taken the issue very seriously (and, of course, followed my advice, for which many bonus points would be awarded (-: ).
