The linked-to page of the multicast HOWTO doesn't say anything about tcpdump.
Tcpdump uses libpcap to capture network packets and, on Ethernet, libpcap supports both:
promiscuous mode, in which the network adapter delivers to the host every packet it sees, regardless of the destination address, and the network stack delivers every packet passing the filter to the capture mechanism, and
non-promiscuous mode, in which the network adapter delivers to the host unicast packets, broadcast packets, and multicast packets it's configured to deliver, and the network stack delivers all of those packets that pass the capture filter to the capture mechanism.
Tcpdump default to requesting promiscuous mode; in that mode, you'll even see unicast packets not sent to your host (as long as you're not on a switched network or are on a switched network but are plugged into a "mirror" port that gets all traffic).
If you pass tcpdump the
-p flag, it will request non-promiscuous mode, in which case you'll only see the packets that your machine "should" get; in that case, if no process has registered an interest in a particular multicast group, you won't see packets sent to that group's multicast address, but, in that case, that's not a bug, that's a feature, as your machine isn't doing anything with those packets.
So if you want to see all packets (unicast packets to all hosts, multicast packets to all multicast addresses, and broadcast packets), run tcpdump (or Wireshark or whatever) in promiscuous mode and, if you're on a switched network, run on a "mirror port" or "SPAN port" or whatever the switch vendor calls it (if it supports "mirror ports").
See the Wireshark Wiki page on Ethernet packet capture for a lot of details on promiscuous mode and switched networks; the information on that page applies to all packet sniffers, including tcpdump, not just to Wireshark.