I'd actually say it is not critical at all. Temps are, humidity not so much. I don't like seeing below 30% or over 70%. I have perfect sheds as long as the RH is not below 53%. Hygrometers are temperamental products. Digital ones should be kept perfect clean and away from dirt and dust they usually do not stay accurate (if they started that way) long typically they start to read high.
I prefer analogue ones. Hair ones are very fragile they should be avoided. The things to look for are METAL face cards (NO paper or card) and a calibration screw. The ability to calibrate the hygrometer means it can accurately be checked and corrected as needed. Something like this,
http://www.amazon.co.uk/Western-Digi...032649&sr=8-18