I have only done a few jobs that used footnotes. One of them was my undergrad thesis, which I did as one document, so all of the footnotes were numbered consecutively. If I had to make an uninformed bet, I'd guess that chapters shouldn't restart at 1, but that's only a guess. Also consider that there are several sets of rules that people can use (Chicago Manual of Style, APA, MLA, Turabian), so the "correct" answer might be conditional.
D Stark wrote:
I don't see any option for InDesign to handle that unless I combine all the chapters into a single file. Am I right?
There is the option to (for example) restart the numbering of chapter 2 with footnote number 8, if the last footnote of chapter 1 was 7. That will require you to always check each document of the book before you output it to be sure your restarts have the correct number, in case you added a footnote to a chapter that will cause the next chapter to need a new start number. You can restart footnote numbers in Type>Document Footnote Options>Numbering and Formatting.
There may be a plug-in that offers better footnote options, but I don't think InDesign's native footnote feature will allow footnote numbering to span book chapters, but I'm using CS5, so maybe newer versions can do a better job.
I recommend you check back here to see if anyone has given a more definitive answer before you take my word for it.
Yes footnotes need drastic improving.
You'll need to go to the Documnet Footnote options in Each Chapter and insert a start number for each one.