I get an 'ORA-00904: invalid column name' error if I run an update or insert statement in the editor and then view a table in the schema browser.
The Oracle client being used is not supported by Toad for Oracle.
Upgrade your Oracle client to a version that is supported by Toad for Oracle.
You can check the System Requirements section of the Release Notes to see what versions are supported. You can find the Release Notes in the C:\Program Files\Quest Software\Toad for Oracle 10.6\docs directory.
These are the supported Oracle client versions as of version 10.6:
Oracle Client 9.2.0.8
Oracle Client or Instant Client 10.2.0.4
Oracle Client or Instant Client 11.2.0.1
Note: Only 32-bit is supported.