I had this problem, BUT I know how to fix it. It is not the mirror compass that is faulty, you probably were on the map on the center console, and clicked on the compass by accident. If you click on the compass, it points to North, no matter which direction you are facing. You have to go into the map again, and click on the compass again. The mirror compass is correct. This is my theory, if it does not work, then the mirror map is probably faulty.

Update from Jul 4, 2015: I also noticed this problem, and it usually does it half the time. Going to my destination it does it, but going home it does not.

The compass in the mirror on our car has not worked properly since the first month we owned the vehicle. At first we tried to reprogram it according to the owners manual. The compass wouldn't allow that to happen and had a flicker to it. The dealer took it in and replaced the mirror.

The compass still wouldn't show the proper direction and the flicker persisted. We took it back to the dealer and they replaced it a second time. This time they swore it was working. We went out into the parking lot and it wasn't. The tech who had worked on our car came out and tried fiddling with it and said it need to be replaced again. Once more we waited for them to order the part and install a new mirror. By this time this is the cars 4th auto dimming rear view mirror with compass. This time they tell us that they've talked to Hyundai corporate engineers and they said that it's a problem that they will have to work out in their labs. They corporate engineers think that it has to do with the compass sensor placement in the car being distorted by contact with a metal component. The thing is that the car has at least 3 different compasses and sensors for each are not linked. Hyundai corporate has not come up with a solution to date.

Of interest is that the loaner 2012 Genesis that our dealer gives us has the same problem. Three years later and it's still not fixed on the Genesis makes me think that Hyundai corporate engineers don't give a care about the problem.

If you look at the photos I posted you can compare the mirror compass with the GPS compass. I also took video which I have not uploaded. The video actually shows us driving in a circle and our car pointing due south and the compass saying north.

Update from Aug 8, 2015: It's not the map. I know that the map has two options for the compass (one is top of map always equals north; the other is top of map is the direction you are facing). I am referring to the compass on the mirror itself and using the GPS map to prove that I am facing the correct direction. Also in AB, Canada our roads are on a north-south, east-west grid meaning that I actually always know which direction I am facing...and the compass is on the mirror is wrong. As a side note the mirror compass will flash every few seconds and change its direction even when the car is not moving. It has nothing to do with the programming of the compass since both 3 techs at the dealership and myself have reprogrammed the compass according to the owners manual. According to the engineers at Hyundai when our dealership phoned them for advice, Hyundai Canada said that the car most likely has a manufacturing defect where the sensor for the compass is not insulated from the surrounding conductive material causing it to malfunction. But for reiteration sake, I am NOT having issues with the accuracy of the GPS unit or the compass built into the tachometer screen. I am only having issues with the compass in the mirror.

Update from Aug 8, 2015: It's not the map. I know that the map has two options for the compass (one is top of map always equals north; the other is top of map is the direction you are facing). I am referring to the compass on the mirror itself and using the GPS map to prove that I am facing the correct direction. Also in AB, Canada our roads are on a north-south, east-west grid meaning that I actually always know which direction I am facing...and the compass is on the mirror is wrong. As a side note the mirror compass will flash every few seconds and change its direction even when the car is not moving. It has nothing to do with the programming of the compass since both 3 techs at the dealership and myself have reprogrammed the compass according to the owners manual. According to the engineers at Hyundai when our dealership phoned them for advice, Hyundai Canada said that the car most likely has a manufacturing defect where the sensor for the compass is not insulated from the surrounding conductive material causing it to malfunction. But for reiteration sake, I am NOT having issues with the accuracy of the GPS unit or the compass built into the tachometer screen. I am only having issues with the compass in the mirror.