Psychology is a strange science in that it's a mixture of people with very unquantitative backgrounds, and those who deal with very complex math and statistics. What many don't realize is that meta-analysis itself really was developed as a method in psychology (even if it technically has its origins earlier with Pearson). This registered replication work is an extension of that, again being done by psychologists. It's probably safe to say that more empirical and statistical research on the scientific process itself has been done by psychologists (along with statisticians and many public health researchers) than any other discipline.
In any event, replication problems happen in other domains as well. This has been documented empirically. It might be worse in the biomedical domain than, say, physics or chemistry, but it's not limited to psychologists. What I see in the neurosciences per se is just as bad, if not worse (because it's ignored more).
I think ignorance of issues pertaining to overfitting, etc. definitely contributes, but I also think that ignorance is pretty widespread, and the problems can be sort of pernicious in that they don't always operate intuitively.