Well that's kind of the challenge, you have to keep a mental note of where you dudes are and be ready to catch your hero when he comes down. There's actually a little radar on the right side of the screen that tells you where they are, but I've never used it. It gets even tougher in the later stages when the buildings are much higher,the speed doubles, and people are falling one after another. You sort of enter this zen matrix mode where you are catching people without even seeing what you are doing (you can tell by the sound effects). But generally the best strategy is to let them die and just concentrating on surviving yourself. Eventually you'll get better at controlling your dude. Depending on which pixel he hits on your net he will fly at a certain angle in the opposite direction, or if you have the big net, straight up, which is very useful. Popping out the other side when you go to the edge is weird though. Doesn't happen on my copy. Maybe it has to do with your controller? Weird.
There are helicopter and key items hidden in specific locations. If you can get the key or the helicopter (which you have to catch when it comes) the stage will end, and you will go to a bonus stage if you get the 'choppa (with a possibility of a 1up). Also if you can get the net upgrade (looks like a plate) you will get a bigger net which helps a lot. Haven't found many of the key/heli locations after stage 15 yet (there are 30 stages in all) but I'm thinking about writing a FAQ for this game as I've made a note of lot of their locations.
For example, there is a copter on the second window from the left and in the very middle in very top row in stage 1 (you have to save the people first), a key on the very left of the top in stage 2, a copter one from the right in the top row in stage 3, a key in the middle of the top row on stage 4, etc.
But yeah, I agree the opening/ending siren sounds are quite annoying. But I love the sound effect for bodies hitting the street, so it kind of balances out.