What can a letter writer say in a teaching letter to make a candidate stand out?
I've served on many search committees in a mathematics department.  At our institution teaching and research are both important, and I wouldn't describe our institution as entirely "teaching focused."  

In my experience, most recommendation letters that address teaching don't show that the letter writer has actually observed the teaching of the job applicant and don't say much about what the applicant actually does in the classroom or how effective this was in promoting student learning.  I'm generally impressed by letters which describe direct observations of the candidate's teaching.  

e.g. "Jane had average student evaluations of 4.0/5.0, which is very good in my department." isn't very helpful (especially since I can read the teaching evaluations that the candidate submitted with the application.)    On the other hand, I'd like to see something like "As the calculus course coordinator, I met with John on a weekly basis and regularly observed him in class.  His lectures were well organized, and he regularly incorporated pair-and-share and other active learning strategies.  In interacting with students he consistently has a positive and encouraging attitude.  I have never had to deal with complaints from students in his sections.  John's students also performed well above the course average on common final exams."