Is it safe to use MD5 in a proof of work system? Here is the POW system: you are given a string and you need to compute a suffix so that first few bits of the MD5 value are all 0. I know MD5 is collision vulnerable, but is it safe to use MD5 here, or, state it in another way, is there a non-bruteforce way to compute the suffix?
Currently, it is probably safe. There are preimage attacks on MD5 but they are only slightly better than brute force. With a proof of work that only requires the initial bits of the hash to match it would likely be easier to use brute force than try to apply any attacks on it.

However, I cannot see a good reason you would do that instead of using a more secure hash function, like SHA-256 – or SHA-256/128 if the output length must match.