I would like to apologize for my delay in my reply as I was not receiving my notices for new support forum posts for about a week. Just reply notices to ones that were already started which is why I’m just now noticing.
0.7.2.6, theoretically should work with WordPress 3.6, especially if it working fine with 3.5.1. Honestly, I’ve never tested the older release on the new WordPress version.
There’s no security implications that I’m aware of using an older version.
If you do upgrade, I only suggest making a DB backup first because Connections will have a couple schema changes it’ll have to make to its tables.
I hope that helps.