lsof will show you the open file handles.
If you know the PID use the -p-p flag.
Eg, on my zsh shell at the moment I see:
alex@smiley:~|⇒ lsof -p 82946
COMMAND PID USER FD TYPE DEVICE SIZE/OFF NODE NAME
zsh 82946 alex cwd DIR 14,12 2414 186278 /Users/alex
zsh 82946 alex txt REG 14,12 1103984 73 /bin/zsh
zsh 82946 alex txt REG 14,12 474672 787843 /usr/lib/zsh/4.3.11/zsh/zle.so
zsh 82946 alex txt REG 14,12 258672 787864 /usr/lib/zsh/4.3.11/zsh/complete.so
zsh 82946 alex txt REG 14,12 120576 787863 /usr/lib/zsh/4.3.11/zsh/complist.so
zsh 82946 alex txt REG 14,12 71264 787838 /usr/lib/zsh/4.3.11/zsh/zutil.so
zsh 82946 alex txt REG 14,12 79968 787852 /usr/lib/zsh/4.3.11/zsh/parameter.so
zsh 82946 alex txt REG 14,12 599280 7719861 /usr/lib/dyld
zsh 82946 alex txt REG 14,12 296980480 12427083 /private/var/db/dyld/dyld_shared_cache_x86_64
zsh 82946 alex 0u CHR 16,0 0t26354 6285 /dev/ttys000
zsh 82946 alex 1u CHR 16,0 0t26354 6285 /dev/ttys000
zsh 82946 alex 2u CHR 16,0 0t26354 6285 /dev/ttys000
zsh 82946 alex 10u CHR 16,0 0t3432 6285 /dev/ttys000
The Type column shows the various file or pseudo file types that might be open, sockets, pipes, etc.
ulimit or limit, depending on system and shell lets you change the number of open files.
