Is it possible to measure the Coriolis force in some helpful way to build a compass?
Indirectly, yes. It is called a gyro compass. When you constrain a gyroscope to spin about an axis in the horizontal plane it will experience a Coriolis like force unless it is pointing due North-South - if it isn't it will slowly align, then stay there, so you can use this as a compass - in fact it is widely used as it doesn't suffer from magnetic deviation.
A very detailed description of the operation of a submarine gyro compass is given at this link. It ought to dispel any doubts you have about whether this works - even at the equator. In fact the only place where it fails is the poles - where it will maintain a constant position relative to the stars (as opposed to remaining aligned with the meridian - because at the poles, meridians point in all directions...)
2$\begingroup$ Unfortunately, it will not work on the equator, and you cannot tell if it is pointing north or south, unless you know which hemisphere you are in. $\endgroup$– LDC3Nov 10, 2014 at 4:07
$\begingroup$ @LDC - I don't think that is right. It won't work at the poles but there is no reason why it would not experience a torque at the equator when the axis is not aligned North-South? And I'm pretty sure it works on both hemispheres... Why wouldn't it? $\endgroup$ Nov 10, 2014 at 4:17
$\begingroup$ According to the University of Illinois "The Coriolis force is zero right at the equator." It does work on both hemispheres, only in opposite directions, so if you don't know you are south of the equator, what you think is north is actually south. ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/fw/crls.rxml $\endgroup$– LDC3Nov 10, 2014 at 4:22
$\begingroup$ The Coriolis force is zero if you move in the plane of the surface of the earth, yes. But a gyroscope rotating with its axis in that plane has parts moving towards the earth and others moving away... Imagine the torque on a E-W pointing gyroscope at the equator and you will see it reorients to N-S. I think I will have to draw a picture to convince you... Give me a bit of time. $\endgroup$ Nov 10, 2014 at 4:25
$\begingroup$ Please see maritime.org/doc/fleetsub/elect/chap17.htm for all the pictures I could hope to draw... $\endgroup$ Nov 10, 2014 at 4:45