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Not sure about the keys themselves if they've already been generated, but even after a key is generated, a lot of situational stuff involves random numbers (session keys, initialization vectors, nonces, etc), and lesser variation in these can make it easier to attack traffic with known content patterns.

This is a very good point, one that I missed in my followup on the FreeBSD-CURRENT mailing list. See also https://www.imperialviolet.org/2013/06/15/suddendeathentropy...

Yes, even with correctly generated keys if you perform DSA signatures with a broken RNG you risk reusing a k value which will leak your private key.

You don't even have to re-use a k value - if the attacker can guess your k value, one signature is enough to recover your private key.