How to force Word to recompute image numbers?

You need to update all references in your document. To do so select all of the document (Ctrl+A) then press F9.

Word 2011 for Mac updates these field values for the whole document before printing. You don't actually have to print the file but just open and close the print dialog via File --> Print... --> Cancel. Don't know if this works for all versions.

I've just come across a scenario where Word had decided that the second figure in my document was Figure 1, and that the first one was Figure 2, and that there was nothing I could do to persuade it otherwise.

The eventual solution turned out to be,

1. Select the second figure and its caption and cut it.
2. Update fields with F9.
3. Paste the figure and caption back in.
4. Update the field in the newly-pasted caption.
5. Fix the inevitable resulting formatting SNAFU.