Bioinformatics : Drawbacks of using ORA(Overlap Analysis)
It really depends on the specific methods you're using. If you're using a pathway-based methodology, I'd strongly recommend reading Khatri et al (2012) (1), which provides a good overview. 

The main issue that's not touched on in that work is that pathway-based methods are highly dependent on the pathway definitions used, and the contents of the pathways are not always what you might expect in terms of their topology (a good example is KEGG's Neuroactive ligand-receptor interaction (2), which contains a huge number of events that look like 'single ligand binds to receptor', with no downstream events).