As you know var_dump()
in addition to value show its data type and length.
Is there any way to log its output to
If you have an Ajax (XHR) call that is generating output with a var_dump() then you can inspect the request in FireBug either under 'Console' or 'Net'. Click the plus sign to expand it and look at the 'Response' tab.
Otherwise if you are putting var_dump() into the main page you are viewing it should just appear in the page as viewed although the formatting might be messed up. Try
echo ''
before the var_dump() or alternatively view the page source rather than the direct output.