Intrusion logging on cable internet

Is there anything special that needs to be set up for a router/firewall to log only unsolicited incoming connection attempts and attacks, and not local broadcast traffic (on the cable internet)? Namely, when I tried either D-Link DI-604 or Level One's 1412, for example, they only logged "Unrecognized attempt blocked from ... to ...". But when I connected ASUS WL500gx to my cable modem, it would log a tremendous amount of traffic, most of which were (I presume) local broadcasts (UDP) from somebody else's IP to What's the deal here?

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