All the recent fuss is not at all about RSA. It is about Dual_EC_DRBG, a PRNG which has no relation whatsoever with RSA.
Some wild speculation has been made about other usages of elliptic curves, for other algorithms, which again have no relation with RSA, except that some EC-based algorithm may be used as replacements for RSA.
Now there is a relation not with RSA, the algorithm, but with RSA, the company, which edits a number of cryptography solutions, including one, called BSAFE, which implements both RSA (the algorithm)(actually the algorithmS, since there are RSA signature and RSA encryption, which are not the same kind of thing), and the Dual_EC_DRBG PRNG. Any software which was using BSAFE for random numbers may be at risk, depending on what kind of randomness they needed.
It so happens that "normal" RSA signatures (technically called RSASSA-PKCS1-v1_5, or "PKCS#1 v1.5") are deterministic: they don't use randomness at all. In particular, they cannot be put at risk by flawed randomness.
The newer "PSS" padding scheme for RSA uses random numbers, but not in a way which is critical to security. As PKCS#1 puts it:
RSASSA-PSS is different from other RSA-based signature schemes in
that it is probabilistic rather than deterministic, incorporating a
randomly generated salt value. The salt value enhances the security
of the scheme by affording a "tighter" security proof than
deterministic alternatives such as Full Domain Hashing (FDH); see 
for discussion. However, the randomness is not critical to security.
In situations where random generation is not possible, a fixed value
or a sequence number could be employed instead, with the resulting
provable security similar to that of FDH .
(emphasis is mine)