Like Star Trek's Starfleet Command, the Galactic Patrol seems generally more interested in police and exploration duty than actual combat, and they rely heavily on Mighty Orbots in this area. The one time GP forces actually engage Shadow forces without the Orbots' help ("Operation Eclipse"), they are soundly defeated.
Rondu's formidable mental powers are demonstrated in "Raid on the Stellar Queen," in which he is captured and used to power a monstrous ethereal creature called a "Thetan," and in "Operation Eclipse," in which he engages in a mental battle with his old friend-turned-traitor, Drennan. Beams of energy emanated from the sigil on each combatant's head-circlet.
Dia is the officer in charge of Earth's defenses, but is frequently dispatched by Rondu on a variety of missions either in lieu of or in support of Mighty Orbots. She jets around in a small cruiser with just enough room for herself and a prisoner. Her only equipment other than her uniform and helmet is a wrist-comm on one hand and a wristband force field projector (for subduing criminals) on the other. Whether or not all this is standard equipment for a GP agent is unknown; Dia is the only field agent we get to see.
Dia never demonstrates any mental powers in any of the episodes, but she does offer to help her father to break Drennan's psionic lock on the Orbots, so it would seem likely that she does possess such powers.
Other than Dia's cruiser, the only GP hardware we see are large transports and a few pod-like fighters ("Operation Eclipse'), and the short-lived Deflectron ("Trapped on the Prehistoric Planet"), a defense satellite capable of projecting an impenetrable force field around an entire planet. We also do see some interesting Galactic Patrol robots organizing the city evacuation in "The Phoenix Factor."