To handle the errors from bigquery I have used - job.errors[0]['message'] and everything was fine so far.
The issue is when you querying and for example, when you divide the value by 0, BigQuery will show you:
QUESTION: By using PYTHON - HOW to pick up this error?

Or, in BigQuery Standard SQL, you can use SAFE_DIVIDE() to avoid error
SAFE_DIVIDE() is equivalent to the division operator (/), but returns NULL if an error occurs, such as a division by zero error
So instead of
SELECT 15 / 0you should useSAFE_DIVIDE(15, 0)