Why do you think Beatty “let the first alarm ride?"
The first alarm occurs when Mildred's friends notify Beatty that Montag has been reading and reciting poetry. We learn of this in Part 3 when he says he let this first alarm ride. It is abundantly clear that Beatty has extensive knowledge of literature and philosophy. He is able to quote classic works without hesitation and he uses these quotes to counter any insights Montag has learned from his readings. In the final scene at the firehouse, while Beatty is doing just this, Faber speaks into Montag's ear saying he is just trying to confuse Montag. Beatty is using quotes out of context in order to challenge the notion that literature is valuable. At the end of Part 2, Beatty hypocritically says "The Devil can cite scripture for his purpose." In fact, this is what Beatty is doing. A few paragraphs prior to this line, Beatty says this:
Read a few lines and off you go over a cliff. Bang, you're ready to blow up the world, chop off heads, knock down women and children, destroy authority. I know, I've been through it all.
Beatty lets the first alarm go because he was once interested in literature as well. He recognizes that people are just curious. As long as they get that curiosity out of their systems and return to the world of banned literature, he will let it slide. Likewise, he lets the first alarm slide, thinking Montag will come to his senses and get rid of the books.