I closed two open tickets related to networking in Linux Kernel. So, I'd write it down in order not to forget.
* broadcast ping problem. After Linux kernel 2.6.14+, the kernel wont' respond to broadcast ping by default. You have to "echo 0 > /proc/sys/net/ipv4/ignore_broadcast_icmp" to enable response to broadcast ping. The default behavior has been changed.
* loopback ping > 32K payload. For small system with <= 16M memory, we use loopback UDP for IPC. But we can't receive packets with 32K+ payload. I wrote a test program to verify the problem. After one day's hack, I found that it is due to a limitation in internal buffer size of skbuff (the internal data structure in Linux network stack). "/proc/sys/net/core/rmem_max", "/proc/sys/net/core/rmem_default". We have to increase the limit on those two entries to allow loopback ping with 32K+ payload. There won't any problem with network ping, as the MTU limitation will eventually split the skbuff and you won't need a big skbuff. The loopback has no MTU limitation, thus it matters.