I'm looking into picking up a digital gyro with sufficient resolution to detect rotation down to 15 arcsec/sec and perhaps a bit better. Alternatively, increasing the sampling interval to 10 seconds or so might permit a bit less resolution. Ultimately, I want to be able to measure the rotation of the Earth which is just a bit over 15 degrees per hour or 15 arcsec/sec. There are LOTS of units in the $20-$80 range with many including 3-axis accelerometers as well as magnetometers and baro sensors and I'd be happy getting a more capable sensor so long as the price is right. I understand that MEMS is capable of detecting Earths rotation but just which model is hard to discern.
Of course, when attempting to measure Earth's rotation it's a good idea to mount the sensor with a polar alignment and if the unit is sensitive enough the angular velocities should help with roughing the polar alignment. Such a sensor might speed telescope alignment, though to get down to sub arcmin accuracy I don't see anything but the highest performance laser gyros being able to do that. But, if getting a rough alignment is quicker then tweaking that by sighting on Polaris and other stars is still necessary.
Brian