An error in printed book is my fault: what do I do?
I designed a kids' activity book for my client. She handwrote all the text correctly and I typed a sentence out incorrectly. She approved the proof before print but that was the 6th draft so I guess both of us were too tired by that stage to spot this error.
If it was her provided text, I wouldn't see it as entirely my fault. But I typed it myself from her correct notes so it is. Should I give a discount? A full refund? She's printing labels to put over the incorrect text. Should I at least pay for that?
It's her responsibility.
That's why you provide proofs that she can freely take as long as she wants to review. A good trick is to make them write by email that they approve the proof. You ask it this way before sending the final print-ready file: "So, is this approved or do you need any more revisions?" She'll respond a Yes, or No. You got your approval and that's enough for you.
If she's a long time client or there's potential for more projects with her, you can offer her a rebate on the next job.
Also, make sure to add a line of text on your proof: Please review this proof carefully, the designer is not responsible for any mistake or omission, etc.
But one thing I strongly suggest: Do not ever type words.
Copy and paste them. It's so easy to make a typo and not see it, and amazingly these mistakes are often made in the titles because people just don't read them at some point! If the text is handwritten, you can type it and have her review it in plain text first. In any way, whenever you add texts yourself, specify to the client she/he must review it, that it was NOT proofread... or pay someone for this and charge the client. You're a designer, not an editor.