Is it possible to change the path of modules/themes installed using an installation profile? I have a site which has a profile which downloads a number of modules using drush make. It adds the modules in the path /profiles/profile_name/modules. 

Is it possible in the make file of the profile to change the path to where the modules and themes are put, so that they are then installed in sites/all/modules and sites/all/themes?
If you have already installed the profile — no, you can't move modules by modifying make file. Profile's .make file is used only during installation process.  

If you want to replace modules from profiles/%PROFILE_NAME%/modules/ to sites/all/modules on already installed copy of Drupal, you can just replace files (with mv or something) and then run system_rebuild_module_data() function to ask Drupal to update modules destination. With Drush:  

drush eval "system_rebuild_module_data();"


For profile installation process — I really don't know why and don't know how to modify .make file. Maybe you can specify 'contrib_destination' property for every project?