Are these run through an algorithm to determine credible threats based on political/religious affiliation, or do they just investigate every random dumb ass with a shotgun who bitches about the President?
There is a score metric. I shit posted about this elsewhere but:
Assassins don't come out of nowhere. There is a threat matrix, where just sitting on your porch and shit posting about how someone should should kill Obama with frozen porkchop doesn't raise too many red flags.
Screaming at the DMV lady about how you want to decapitate the governor and fuck his headless torso will also probably get you noticed, but if you've had no LE run-ins, probably no visit.
Now, calling a government office and leveling a specific threat is not the sort of thing a sane person does, and usually indicates a level of escalation that approaches thought out action.
I knew a guy who worked adjacent to law enforcement in a city the president visited. Before the visit, the local cops gave the SS access to their arrest & reports records - which combined with the SS's own secret sauce resulted in the SS giving the local cops a list of individuals and "We want to know where these guys are at all times the President is in or near your jurisdiction. We're sending some agents to assist with that"
The not-quite exception that proves the rule is John Hinkley, who DID come out of no where. He had no run ins with law enforcement or any criminal record. He was also abysmally awful in his attempt, missing his target with all his shots and only wounding Reagan with a lucky ricochet off the limo.