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.

If Track Changes are turned on and tables, figures, and associated captions have been modified, I found I had to accept those changes before the suggestions above worked.

Ctrl-A then F9 will only work if you have added the captions using the add caption option when right clicking the image.

If you have added lines manually saying

Figure 1 - blah blah

then Word won't renumber them, because they are just another line of text. You can tell which captions are added and managed by Word and which one aren't by toggling on field codes. I do this by hitting Ctrl-A, then right clicking on a caption or blank area and clicking "toggle field codes".

Captions which have been created by Word will now look something like

Figure {SEQ Figure * ARABIC} - blah blah

instead of having a number. If your captions do not show this, then Word won't renumber them. So erase them and replace them with captions created using the Insert Caption option.