Some data returned by SQLite cannot be freed using standard methods.  The data are error messages and table data.  A flawed but non-crashing solution is to add two new data types:

+	[Compact]
+	[Immutable]
+	[CCode (cname = "char", const_cname = "const char", free_function = "sqlite3_free")]
+	public class sqlitestring {
+		[CCode (cname = "g_strdup")]
+		public string to_string ();
+	}
+
+	[Compact]
+	[Immutable]
+	[CCode (cname = "char*", const_cname = "const char*", free_function = "sqlite3_free_table")]
+	public class sqlitetable {
+	}

And change the method signatures of exec and get_table:

-		public int exec (string sql, Callback? sqlite3_callback = null, void* data = null, out string errmsg = null);
+		public int exec (string sql, Callback? sqlite3_callback = null, void* data = null, out sqlitestring errmsg = null);

-		public int get_table (string sql, out string[] resultp, ref int nrow, ref int ncolumn, out string errmsg);
+		public int get_table (string sql, out sqlitetable resultp, out int nrow, out int ncolumn, out sqlitestring errmsg);

The error message part works fine like this, the table part doesn't cause errors, but is unusable in Vala.  If you access the table data with an [Import ()]ed C method, it does work.