Is it ethical to ask students to proofread a textbook?
Is it ethical to give a grade (or extra credit) based on student feedback?
I think the key question is, will reading draft material from your textbook help students towards their understanding of the subject of this class?
If yes, then it honestly sounds like a great exercise to me. Not only does it force the students to actually read some material related to the class (albeit in an unpolished draft form), it also could allow them to "check" their understanding by comparing the draft with the material they are already familiar with. Some suggestions:
It seems best if they are asked to read material that you have already covered in class and that there are other sources on; that way they are not just completely lost, but they have something to compare to and a way to reliably detect errors.
If this is part of the grade (extra credit or otherwise), I think it should be mainly based on completion, not on how many errors and typos they find. You could also ask them to write a "summary" of the chapter to check their understanding and thoroughness.
If no, then it is unethical. Your job as a teacher is to help the students learn the material, and using them as free labor to proofread your book is inappropriate.
This could be the case, for example, if the book is not exactly on the subject of the material that the class is covering, or if it is in such an unpolished form that it is difficult to get anything out of while still a student, and not an expert on the material.
In practice, you will receive great feedback from a very small proportion of the students (and this subset will consist almost entirely of students who will do well on the course regardless). But even the weakest students can and will make perspicuous observations, or point out gaps in your explanations, that will be helpful. And then many students will be hard-pressed to contribute anything.
If any credit at all is traded for feedback, you actually raise the threshold for students who are aware they are not among the top and hence afraid of saying something dumb. The "swots" might go into overdrive, which generally produces lots of great feedback, but you feel you are abusing the time and kindness. The majority who has no substantial thing to contribute might feel compelled to manufacture something.
The "extra" idea does not mitigate against the latter problem, since students will evaluate every bit of possible credit in terms of the relative effort. Any carrot being dangled is far play.
So: my answer based on experience over several books and years of teaching: do not skew or degrade the feedback you could be garnering with any of these extra credit arrangements (quite aside from ethics which has been well addressed in the other answers). Use the book-in-progress as lecture notes, make it very clear that you are aware it is still teeming with mistakes, and that any and all comments are hugely appreciated.
At the end, you will know the main feedback contributors by name. They will come to you for recommendation letters, career advice, and so on. And then you will be able to reward their kindness in kind. Such is not a bribe; the praises you have to sing about such a student are genuine!
It is ethical to ask students to proofread a textbook. It isn't (generally) ethical to grade students based upon their feedback having proofread (unless their is an agreed-upon educational basis).
Some students will read the draft of your textbook, especially if it is required reading. You can ask students that do read your book to provide feedback and you can offer to include any students that do with an acknowledgement.