PL/SQL block fails in job but succeeds in SQL*Plus
What happened is that I had all the permissions and privileges set right except I forgot to create the directory on the second node too.

So whenever the job ran on the second instance (which it by chance did) the error was raised that the file could not be written.



Of course it had to be as simple as that but I want to post it as an answer anyway.

When working with an Oracle RAC your mantra should always be "Keep in mind the other instances."