From Wikipedia's page on criticism and limitations of BOLD:
Although most fMRI research uses BOLD contrast imaging as a method to determine which parts of the brain is most active, because the signals are relative, and not individually quantitative, some question its rigor. Other methods which propose to measure neural activity directly have been attempted (for example, measurement of the Oxygen Extraction Fraction, or OEF, in regions of the brain, which measures how much of the oxyhemoglobin in the blood has been converted to deoxyhemoglobin[(Yablonskiy & Haacke, 1994)]), but because the electromagnetic fields created by an active or firing neuron are so weak, the signal-to-noise ratio is extremely low and statistical methods used to extract quantitative data have been largely unsuccessful so far.
The wisdom of discarding the low-frequency signals in BOLD-contrast imaging came into question in 1995, when it was observed that the “noise” in the area of the brain that controls right-hand movement fluctuated in unison with similar activity in the area on the opposite side of the brain associated with left-hand movement [(Raichle, 2006, 2010)]. BOLD-contrast imaging is only sensitive to differences between two brain states.
Raichle, M. E. (2006). The brain's dark energy. Science, 314, 1249–1250.
Raichle, M. E. (March 2010). The brain's dark energy. Scientific American: Mind & Brain. Retrieved from: http://www.scientificamerican.com/article/the-brains-dark-energy/.
Yablonskiy, D. A., & Haacke, E. M. (1994). Theory of NMR signal behavior in magnetically inhomogeneous tissues: The static dephasing regime. Magnetic Resonance in Medicine, 32(6), 749–763. Retrieved from: http://siba.unipv.it/fisica/articoli/M/MagneticResonanceInMedicine1994_32_6_749.pdf.