The main danger is if the community trusts such an organization too much. For example- if everyone assumed the client version put out by the organization was trustworthy, then there is serious danger. A group as you propose should probably exist, but the community should remain skeptical of it, and always constructively critical.
I thought of the exact same thing, now is the time to make one or more services which sole purpose is to constantly review the downloadable official client for changes, and alternative clients too. As long as these checks are in place, it should be difficult to sneak in backdoors. Such checks are no distrust, but rather a salute to the current developers, and the very nature of bitcoin.
There are discussions of this in one of the other threads around here. Great idea. If I'm not drunk before my server comes back up (they say it is a multi-state outage, so don't hold your breath), I'll write a PHP script to fetch and compare signatures. Actually, I think someone might have already posted one.
The problem is that all of the signatures and the binaries all come from the same shadowy cabal of secret developers that operate from their hidden lairs in the logged public IRC channel and logged public mailing list.