For what it's worth, I just applied all the current updates on one of my 2 JR sites, seemed to go fine.
Because there were so many updates, i did it like this:
If there's aCore update first, i run that and then do an integrity check.
Then I did half the updates, ran another integ check, then finished all the updates and ran a final integ. check.
Also, I always click one update at a time. I find it's always better than clicking the "update all" button.
-- ...just another satisfied Jamroom customer.
Migrated from Ning to Jamroom June 2015