It looks like the most problematic social science papers in recent years have been on the topic of priming effects (example here and sarcasm there and my earlier comments yonder). This research is commonly cited by people claiming free will doesn't exist.
There's another problem field in social science: neuropsychology. It is noted for small sample sizes and being used as an excuse to disbelieve free will.
We need a meta-analysis. Is there a correlation between whether the media reports of a social-science study emphasize its supposed challenge to free will and the shoddiness of the study? Shoddiness might be measured by either the smallness of the samples or the lack of replication.