An incident has previously been reported where the signal from the Navstar 43 Global Positioning System (GPS) satellite contained phase anomalies in such a way as to mimic ionospheric scintillation. We have observed another 25 events from the same satellite, plus events from three more satellites. Our data includes simultaneous observations from widely spaced receivers (up to 6,590 km apart), from different manufacturers, further ruling out the possibility of local effects. Two of the events involved a satellite (GPS IIF SV-2) broadcasting the L2C signal. This signal contained phase deviations matching those of the L1 signal, but with a 120/154 multiplicative factor. This rules out the possibility of a genuine ionospheric scintillation event, as it does not match the plasma dispersion relation. It does, however, agree with what can be expected from an anomaly in the satellite's oscillator. While the previously reported event could be dismissed as a freak occurrence, it is now apparent that these events are a persistent phenomenon. They have the potential to corrupt geophysical research with false data and to generate false alarms in systems to forewarn of GPS outages due to scintillation.