Is any group of bits in a SHA-1 hash more/less unique than another? Is there any bias in certain parts of the hash? E.g., first n bits are more/less unique than the last/middle n bits? Is there any particular property of any group of bits that makes it more/less unique?

Thanks
Yes in a sense in terms of the Hamming weight/Hamming distance. This relates to how the changes of one bit or series of bits affect others. While there is also an avalanche effect counteracting many n string bits attacks, Hamming dictates some attacks to be more successful on certain n bit strings and thus certain n bit strings more vulnerable to exploits:

http://people.csail.mit.edu/yiqun/SHA1AttackProceedingVersion.pdf

http://www.sciencedirect.com/science/article/pii/S0166218X02005887