Depending on what your workbook's displaying,
Edit > Find [#] (i.e. enter the hash sign # as your target text)
Search: [By Rows]
Look in: [Values]
may be less of a pain. In most of my workbooks, the only cells displaying the hash sign are error messages, and as far as I know, all Excel error values (#DIV/0, #NAME?, #REF! etc.) display text starting with #. Even if you have dozens of hash signs in non-error cells, this will be a lot faster than having to wade through the Edit > Go To… dialog on every sheet.
If you want to search for errors without recalculating, you may have cells which display a calculated value that's destined to turn into an error. For example, enter =2+C4, then delete column C. If recalculation is set to manual, the cell will continue to show an unchanged value, but the formula will become =2+#REF! You can find cells in this state by changing the search parameter to Within: Formulas. This can stop recalculation from propagating a cascade of #REF! errors that takes a long while to unravel.
Hope this helps.