You will have these problems if you have safe mode on.
If it's turned off and you have set the 'chmod 777' on the appropriate directories then all is well.
I have my joomla working fine (1.0.10) and with safemode on (all php_admin_values except 'safemode On' to make CMS easier to work with).
Another option if you really want safe mode on is to use safe mode in GID mode and then chmod g+s the directories and it'll always work which I did but then opted for the simpler version. suphp was too much of a pain to get working for me at the time.