The challenges that are faced in biomarker discovery studies are working with relatively small number of samples. Then the variability issue is a problem like variable readouts, test variability, batch effects and clinical annotation. Next, getting a well curated data is also a big challenge. Moreover, sample curation is not uniform particularly when one has to perform post-hoc analysis.
Mass Spectrometry can help overcome some of the issues. It is an analytical method that can be used for higher throughput. It can reduce variability and also avoid false positives and reduce false negatives. The issue of sensitivity and specificity can also be taken care of.
I'd say one of those is a challenge directly detecting weak (but important) phosphorylation signals in complex biological mixtures without doing enrichment via IP or some other affinity purification steps.
Biomarker discovery, to begin with, is challenging because of the amount of the biomarker in presence of many fold excess amounts of other species. Remember that Prostate Specific Antigen was discovered using Elisa approach.
Mass spectrometry does not do well in detecting compounds/biomarkers in the midst of very abundant eg., serum or plasma constituents. It is a very sensitive tool, however, it requires elegant and thought out sample preparation steps up front. If you are working with tissue samples, as Malcolm Nobre emphasized, the amount of material can be limiting step. Enrichment and or targeted analysis may be the way to go with mass spectrometry approach.