The p prints the randomly chosen line -- wc -l is the number of lines in the file, (random % lines-in-file) picks a random one, 'sed -n 30p' prints the 30th line.
Problem with this (and probably with the aspell version too, but I can't test that just now): $RANDOM only generates a number from 0 to 32767, but /usr/dict/words has (on my Mac) 235886 words.
sh -c 'cat /usr/share/dict/words | sed -n $(echo $((`cat /dev/urandom | od -N3 -An -i` % `cat /usr/share/dict/words | wc -l`)))p'
This is closer, although you might get sed: illegal option occasionally, I guess. I'm yet to learn how to generate a random number within given limits with bash. Oh wait, we can use Python can't we?
sh -c 'cat /usr/share/dict/words | sed -n $(echo $((`python -c "import random; print random.randint(1,234935)"` % `cat /usr/share/dict/words | wc -l`)))p'