You are correct console.log isn't helpful because they run server side. There are two methods that I use to debug them.
1. Add them as response tokens. This is easy to do: target > setup > response tokens enable the profile you want to debug. Now any time you load a page for your site with Target on it part of the response from Target will contain your value for the given profile script.
2. The other option is to use the mboxTrace debugging tool. This requires the an authorization token found here: target > setup > implemenation > authorization. Then you add these 2 parameters to your page url after the "?" mboxTrace=window&authorization=YOURTOKEN.
This is a little more informative than the response token because you get a before executed snapshot and an after snapshot of your profile. It will also show all the profiles availalbe for your profile.