One of the most dangerous aspects of Venom is that he doesn't set off Spider-Man's spider-sense. The explanation for this was always that it had once been his costume and being in proximity to him, his warnings did not register the symbiote as a threat.
But when Spidey first gets the symbiote, it does set off his spider-sense as seen here:
What the heck is that--? And why is it making my spider-sense tingle?
So what happened?