It's hard not to be hard on Dr. Silberman. On the one hand, he ignores Reese's warnings about the Terminator coming to find Sarah at the police station. When no one listens, the Terminator ends up doing just that—and murdering every officer in the building in the process.
On the other hand, if someone told us he'd been sent from the future to protect the mother of humanity's savior from a killer cyborg sent to assassinate her, we'd agree with Silberman's assessment that he's more cuckoo than a Coco Puffs factory.
Ultimately, Silberman is ineffective at his job as a criminal psychologist because he doesn't care about helping the people he's brought in to analyze. It's a job for him, something to finish as soon as possible—unless he determines there's a way he can profit from it.
Vukovich hints at Silberman's disregard for those he analyzes when he says, "That guy Silberman cracks me up." The line hints at Silberman's habit of making a joke of his patients' psychoses. For example, he asks Reese why he didn't bring any "ray guns" back from the future, a line that obviously disregards Reese's paranoia. It's not the best way to treat a patient.
Silberman's desire to use his patients to further his own career is further evident when he says, "This is great stuff. I could make a career out of this guy!" We mean, that's pretty self-explanatory, folks.
Silberman leaves the police station just as the Terminator arrives to prove Reese's story, meaning he lives to psychoanalyze another day. Unfortunately, as we'll see in Terminator 2, he hasn't learned his lesson, and he continues to disregard his patients' feelings while using their paranoia to benefit his own career.
We don't want to give anything away, but if you can wait for the sequel, fate will serve this guy his comeuppance. We promise.