I followed the instructions here: http://crazytoon.com/2007/07/23/mysql-changing-runtime-variables-with-out-restarting-mysql-server/ but that seems to only set the threshold
MySQL Manual - slow-query-log-file
This claims that you can run the following to set the slow-log file (5.1.6 onwards):
set global slow_query_log_file = 'path';
The variable slow_query_log just controls whether it is enabled or not.