We address two issues that limit the quality of time and frequency transfer by carrier phase measurements from the Global Positioning System (GPS). The first issue is related to inconsistencies between code and phase observations. We describe and classify several types of events that can cause inconsistencies and observe that some of them are related to the internal clock of the GPS receiver. Strategies to detect and overcome time-code inconsistencies have been developed and implemented into the Bernese GPS Software package. For the moment, only inconsistencies larger than the 20 ns code measurement noise level can be detected automatically. The second issue is related to discontinuities at the day boundaries that stem from the processing of the data in daily batches. Two new methods are discussed: clock handover and ambiguity stacking. The two approaches are tested on data obtained from a network of stations, and the results are compared with an independent time-transfer method. Both methods improve the stability of the transfer for short averaging times, but there is no benefit for averaging times longer than 8 days. We show that continuous solutions are sufficiently robust against modeling and preprocessing errors to prevent the solution from accumulating a permanent bias.