Does it make sense to block RSA keys under 1024 bits? A paper I found (http://eprint.iacr.org/2012/064.pdf, which was submitted to a cryptography conference about two years ago), is based on the analysis of some 7.1 million 1024-bit RSA keys published online. By subjecting the modulus of each public key to an algorithm first postulated more than 2,000 years ago by the Greek mathematician Euclid, the researchers looked for underlying factors that were used more than once. Almost 27,000 of the keys they examined were cryptographically worthless because one of the factors used to generate them was used by at least one other key.

As these findings were related to 1024-bit RSA keys (and even those show some points of weakness), does it make sense to generally block all RSA keys under 1024 bits to enforce/strengthen used crypto?
Those findings were based on a broken PRNG. A broken PRNG affects all keys generated on such a device, no matter the size or the algorithm.

Common primes were how the problem was detected, but the problem itself is unrelated to primes or RSA. If RSA keys of a specific size where affected, that's only incidental because that's what the broken devices generated. 

Blocking keys smaller than 1024 bits can be a good idea, because their security margin against factoring attacks has grown pretty thin, even when they're correctly generated. But that threat isn't related to the paper you link.