Finding hash almost-collisions
Since the output of the configuration of Skein is 1024 bits, we would expect to get 512 bits correct just by random hashing. So the question is, what is the probability of getting 640 bits correct? From that we can figure out how long it would take for that to occur.

There are ${1024 \choose 640}\approx 4.16\cdot 10^{292}\approx 2^{972}$ ways this can happen out of $2^{1024}$ different outputs. If we assume the probability of each output is $1/2^{1024}$, then the probability of getting one of those outputs with 640 correct bits is approximately $2^{972}/2^{1024}=1/2^{52}$. So, perform $2^{51}$ hash function calls and you have a $.5$ probability of getting one of those outputs. That sort of work factor should be do able with lots of hardware (supercomputer, GPUs, etc) in 24 hours. As Paulo said, the problem is embarrassingly parallelizable.