I have seen a number of résumés of doctoral students, but only a few of them listed their evaluation scores when presenting their teaching experience.
- How important are these scores in evaluating the teaching capabilities of a student?
- How does one ensure that the students are sincere in their evaluations?
In case a professor does a slipshod work of a course, not teaching in depth or cramming a lot of syllabus in a short time, there is only so much a TA could do to salvage the course for the students.
- How does the TA make the best of a bad job in such a situation?
- Apart from holding weekly office hours and lenient grading(!), what is the maximum a TA can do, after all?
Frankly, I don't place much weight on an isolated number; it doesn't tell me much in practice about a student's teaching abilities. That would have to be judged via direct interaction—watching them teach or otherwise interact with students. It's really impossible to expect students to be honest in their evaluation, unless they've provided comments; then you can at least see how much they've written; the more extensive the comment, the more likely it is to be sincere.
As for what to do when a professor does a bad job, I don't think that it really makes that much of a difference in the nature of the TA's responsibilities; the main change is in the intensity of the work required. The TA, along with the professor, is responsible for helping students learn the material. If the professor isn't doing an adequate job, then that means the TA will probably need to work a bit harder and dedicate more time to achieve that goal. However, the TA should make sure she is taking care of her other requirements and needs at the same time. The TA position shouldn't consume someone's entire life (unless they are paid accordingly!).
One possibility for how to do things, though, might be to prepare review sheets and guides based on the lecture material (or what the lecture material should have been). This will be good review, both for the TA and for the students!