My Note 3s have never had a problem with the GPS hardware or software (GPS Status, Maps, etc.) GPS Accuracy? If you aren't using some method of enhancing the accuracy of the GPS (carrier phase tracking, millimeter GPS, etc.) the accuracy is only as good as the atmospherics. GPS measures the time it takes the GPS signal to get from the satellite to the receiver. While it's true that the signal travels at the speed of light, that speed varies depending on the medium. (Light travels slower - by a very tiny amount, but enough that GPS has to account for it) near the planet than it does in free space. (A masscon "bends" the signal more, making the path longer, for instance.) So unless you're looking at the HDOP (the horizontal dilution of precision), you can't tell whether you're dead on or a few meters off in any given direction. That difference can be greater than the difference between a phone with a "good" GPS and a "bad" one. (And if the phone doesn't have eGPS, you probably won't get a reading indoors. Conversely, if it does, the indoor reading will be a lot less accurate than when it's actually reading signals from a few satellites.)
If you want accurate GPS, get a GPS receiver that uses ground stations for correction. (The ground station knows precisely where it is and broadcasts that location, so the GPS can see how far off its calculations are. The system [with a few other enhancements] is so good that locations can be determined within a millimeter. You can know where the edge of your property is plus/minus the size of a grain of dirt.)