The other day I needed to do some DHCP troubleshooting. I have yet to learn all that tcpdump can do (I know it can do this filtering as well), so I at this time do most of my filtering in wireshark. 
Say you are looking for just the packets pertaining to one particular mac address. You can view these by using the following wireshark filter:
bootp.hw.mac_addr == 00:aa:bb:cc:dd:ee
I have found this to be very useful when I am trying to debug issues client devices maybe having or looking at the dhcp options being sent to a dhcp server.