What Anders said, basically. Keep in mind that GPS uses a modification of the "great circle" method to locate a receiver. One satellite will give you a circle of possible solutions - constant distance from the satellite. Two satellites will give you two possible solutions (where the great circles intersect) while three satellites will give a fairly unambiguous position coordinate. Four satellites are generally required by GPS receivers to give a result because the clocks need to be synchronized as well in order to calculate both position and velocity.
If the GPS receiver displays a calculated position based on only two satellites (and it's really up to the software to ensure it's done correctly) you'd get two possible locations, but due to timing and position of the satellites, it shouldn't be a 180 degree error - the satellites aren't high enough to give solutions for 1/2 of the globe with only two signals. Seems to me there is something else in the software is mis-calculating the solution.
Commercial GPS receivers don't do a very good job of showing elevation either - the error is about 10x worse than that of the lat/long measurement. My point was that you're not going to get a 180 degree error in lat/long just because of an incomplete data set. It must be an error in the software.

