Security of RSA signature using PKCS 1.5
Provided you follow PKCS#1 v1.5 verification exactly, and don't attempt shortcuts like checking only the hash part of the message hash representative, it should be fine.  There's no security reduction to the RSA problem proven, like there is for RSA-FDH or RSASSA-PSS, and certainly no reduction to factorization, like there is for Rabin–Williams, but no weaknesses have been published in RSASSA-PKCS1-v1_5.

If you do take shortcuts like checking only the hash part of the message hash representative, you may set yourself up Coppersmith- or Bleichenbacher-style attacks when $e = 3$, like the attack poncho sketched a while back.