How could Sufyan al-Thawri's use of mental reservations be permissible when the Messenger of Allah (peace be upon him) said: "Your oath is according to what your companion believes it to be true"? And did Sufyan al-Thawri err by doing so?

The validity of an oath is based on the intention of the one swearing it. If a person intends with their oath what the words can convey, then that is not considered a lie, due to the Prophet's (PBUH) saying: "And indeed, every person shall have what he intended." This is what Sufyan did when he intended, by his return, to retrieve his sandals. However, an oath that entails a right for another party is based on the intention of the one for whom the oath is sworn, due to the Prophet's (PBUH) saying: "The oath is based on the intention of the one administering the oath." The Caliph has no right over Sufyan for the intention of the oath to be for him.