Dynatrace categorizes errors into the following types:
To set up how errors are captured, edit your application, and expand the Errors section. Select the required error type, and then configure an error to be captured, included in Apdex calculations, or considered for Davis AI problem detection and analysis.
If you want to see the events you can receive, for further detail you can go here
For each type of event you can see the Applicable Dynatrace entities
yes, you can also filter for application in Problems.
Log Errors can be configured from the Logs menu option.
You need to configure a log source and define what you want to search.
Hope it helps.