Some of our users got error message from Coveo, but we can't reproduce.
Is it any logs in cloud platform? How can I get information about errors?
If you have the analytics component properly configured and logging in the cloud platform, the UI will log those kind of errors as a Custom Event.
They should be available, with the error message, unless it's an error related to invalid token or authentication for example (as we cannot log an event if we do not have the correct credentials to do so).
In that case, if the end users can click on the "More information" button, and send you the detailed error message, you should be able to get access to the complete error message returned by the API.