Chip, I'm posting this from Debian so that I can cut and paste some info. I'm not using Knoppix, as I said I have not run Knoppix recently, but I believe that Knoppix and Debian will have the same results here. I am connecting by DHCP to a Dlink router.

I have never had any occasion to use route and am not clear why you are using it either. When I get my DHCP setup I get a netmask and other settings from the router. That info can be seen by looking at the output of ifconfig (only the portion that deals with eth0 is shown here):
Code:
k6:/home/harry# ifconfig
eth0      Link encap:Ethernet  HWaddr 00:A0:CC:E8:48:D3
          inet addr:192.168.0.103  Bcast:192.168.0.255  Mask:255.255.255.0
          inet6 addr: fe80::2a0:ccff:fee8:48d3/64 Scope:Link
          UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1
          RX packets:6525 errors:0 dropped:0 overruns:0 frame:0
          TX packets:2751 errors:1 dropped:0 overruns:0 carrier:2
          collisions:0 txqueuelen:1000
          RX bytes:7402966 (7.0 MiB)  TX bytes:191431 (186.9 KiB)
          Interrupt:10 Base address:0xe800
Note that the netmask is what it should be for a normal private network using a 192.168 address and having at most 254 users (253 and the router).

Note also that my router is handing out addresses in the 192.168.0.x range while yours is handing out addresses in the 192.168.1.x range. This is normal and I have even seen some routers that default to the 192.168.2.x range and you likely can set this to any third number that you want in your router setup. It is not a problem that we have different numbers here.

I read through the man documentation for route. I see there plenty of example with a netmask, but none that use a netmask of 0.0.0.0.

I couldn't see anything in the man pages to just get route to show me information, so I just tried the command route with no other input. It outputted this:
Code:
k6:/home/harry# route
Kernel IP routing table
Destination     Gateway         Genmask         Flags Metric Ref    Use Iface
192.168.0.0     *               255.255.255.0   U     0      0        0 eth0
default         192.168.0.1     0.0.0.0         UG    0      0        0 eth0
Note that there indeed is a 0.0.0.0 in this output, but it is called a genmask, not a netmask. If you Google the term genmask you will quickly find that the routing tables is using this as a mask differently than a normal netmask and that 0.0.0.0 is simply the general case default that the routing table uses if nothing more specific matches. So I guess this is why it is working for you, but I have no idea why you need to use the route command at all. I and most other people here using routers do not need to.