That depends on what process has produced these errors.
Typically, any errors produced while processing a SOAP request will be captured in web@default log file. The file is located in your <CampaignFolder>/var/default/log/web.log. It is also available through the Console. However, errors, produced by workflow component, will be captured in the workflow log table xtk:workflowLog. Batch jobs have their own log table xtk:jobLog, and so on. Plus, some processes, like MTA, MTAChild or SMS will produce their own log files as well.