When I clicked on the Data tab for any tables on certain schemas, I get "ORA-00900: invalid SQL statement."
The version of Toad you are running does not support the Oracle client that you have installed. Typically the Toad version is older than the Oracle client. For example running Toad 8.0.0.47 against 10g will have this effect on some schemas.
This is caused by a newer Oracle client not supported by Toad. Check the Release Notes of your Toad to see if your client is supported.