The following code raises OperationalError exceptions:
python -c 'import sqlite3; sqlite3.connect(":memory:").execute("bad
syntax")'
python -c 'import sqlite3; sqlite3.connect(":memory:").execute("SELECT *
FROM no_such_table")'
python -c 'import sqlite3; sqlite3.connect(":memory:").execute("SELECT
no_such_column")'

But ProgrammingError should be raised, as per PEP 249:

        ProgrammingError
          
            Exception raised for programming errors, e.g. table not
            found or already exists, syntax error in the SQL
            statement, wrong number of parameters specified, etc.  It
            must be a subclass of DatabaseError.

I have created some naive patch, that makes sqlite module raise
ProgrammingError for SQLITE_ERROR code. But I don't know, whether it
might raise ProgrammingError in situation, when OperationalError should be.

Sqlite docs says: 

#define SQLITE_ERROR        1   /* SQL error or missing database */

and I don't really know, whether missing database is operational error
or a programming one. Seems like the first one, but this would error
message string parsing, that doesn't seem to pretty. Could anyone
suggest me, what else could be done?

The error code SQLITE_ERROR from SQLite is used for "runtime errors".
These can either be caused by the programmer (table does not exist, SQL
contains errors) or they can be other problems like constraint
violations etc.

To differentiate these we would need to parse the error message returned
by sqlite3_errmsg(). This is a path I don't want to go: it's hard to get
this right across current and future SQLite versions.

So I'm closing this issue as wontfix.