ok, ok, ok ... so here are some ideas :
1st and most important) CHECK YOUR ENV !!
be VERY careful because when using cron, you rarely have the environment you think you have. if you're using root crontab, what I usually do is, in the crontab, call a shell like :

10 12,14 * * 1-6 /home/dir1/dir2/launch my_script.sql >/dev/null 2>&1

that way you call a script called launch, which just does :

-----
FILE=$1
export ORACLE_HOME; ORACLE_HOME=...
su oracle -c "$ORACLE_HOME/bin/sqlplus -s user/pwd @$FILE"
-----

that way I am sure that my env is correct.
I guess you can do exactly the same using exp instead of sqlplus, the idea is just to be sure that the env is correct

2) check you have enough space left on device to create dump file
3) check that listener.ora file does not contain GLOBAL_DBNAME parameter