Is it possible to log down error statements in MYSQL?

Question

So that I can just check the logs to see which statements are wrong at a unified location.

Answer 1

Have you read the documentation for the MySQL error log?

Answer 2

If by "which statements are wrong" you mean "which queries", I don't think the error log helps: it logs mysql starting, stopping, crashing, checking or repairing tables... I think you need to use the general query log and post-process it yourself (with a script or something) to extract errant queries only.