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 255.255.255.255. What's the
deal here?