An RFID chip does not contain a GPS transmitter. In fact it only transmits a serial number in response to an activating receiver that is within a few feet of the chip.
Phoebe's mother states that she injected the RFID/GPS chip 2 years before. That injection site should have long since healed, and not left an open wound 2 years later.
While in the hospital, Phoebe asks Calleigh if the doctors and nurses are going to tell anyone she's at the hospital, and Calleigh replies that she has spoken to them and as long as the case is being investigated they won't tell anyone where she is. Due to patient confidentiality laws, hospital staff would not be allowed to discuss any patient unless it is necessary for her care. If they did discuss her with anyone without Phoebe's consent, they could be fired and brought up on charges.
When confronted by the police that Phoebe was kept sedated with haloperidol, her doctor states that Phoebe had episodes of mania being treated by it. Haloperidol is a major tranquilizer and antipsychotic, not an anti-manic medicine. Lithium carbonate is given for mania, while haloperidol treats schizophrenia and a real doctor should know that. Lithium is not sedating and haloperidol is one of the least sedating antipsychotics.