First things first:
Since I wrote it myself I think it is perfect and I cannot detect its possible flaws and mistakes.
It is imperative that you have someone else read over your statement with a critical eye and with the experience to provide quality feedback. You'd be surprised at what you can miss in your own writing, and how the tone may come across different to others.
Which topics would members of search committees like to see in a teaching statement?
This will be dependent on the type of department you are applying to -- at many institutions, research ability trumps teaching, and your statement might not count for much (see below for a caveat about being too gung-ho). Assuming the reason you are asked for a teaching statement is because the department that is hiring does value teaching, I suggest the following:
Demonstrate your understanding that math is difficult for some students, particularly as it gets more abstract. If you can, provide a brief example of a topic that was hard to teach and how you ended up teaching it.
Provide examples of how you changed your teaching based on student feedback or your own assessment. Showing that as a professor, you'll continually try to improve your teaching goes a long way.
Talk about curriculum development -- if you have ever designed a course, make sure you mention it. Describe what you enjoyed about the course development process, and how you addressed the challenges.
Try to convey your passion for teaching -- some of the best teachers are the most passionate, and if you can get that across (only if it is true, of course!), all the better.
Which mistakes in a teaching statement can ruin an applicants' chances for getting an interview?
As with any writing, poor grammar demonstrates a lack of attention to detail (or ability), and that will torpedo your application. Again, have others read it over and provide feedback.
If you are applying to a school where teaching takes a back seat to research, don't make it sound like you live for teaching; you don't want to say that you've stayed up all night crafting the perfect lesson when you should have been doing research.
Don't be boring! This could be a difficult one depending on your writing style. I've seen teaching statements that made it sound like the teacher would be the most boring professor in the world. Again, examples from your own teaching can help make the writing more interesting.
Finally, your teaching statement can be more personal than your research statement, so it is okay to let that come out a bit more. Demonstrating why you'll be a good teacher is the most important part, and this should be apparent in the essay.
Edit: I should add -- as with any other letter or statement, you should feel free to craft different letters for different jobs. If you're applying to a college where professors teach three or four classes per semester, you can expect they will pay more attention to your teaching statement, and you should taylor it appropriately.
