First of all, I would recommend using IDE (IntelliJ or Eclipse) for coding. It can work in parallel with Studio - scaffolding and visual design in Studio, writing code in IDE. So you will be able to use code completion, refactorings, and see errors instantly.
As for the compiler output - when you restart or build your project the compiler output is in the Messages window, you cannot miss it. It should be like this:
:app-web:compileJavaD:\work\tmp\cuba-sample-customer-phones\modules\web\src\com\company\sample\web\customer\CustomerEdit.java:28: error: ';' expected
phonesTableCreate.setAfterCommitHandler(entity -> makeSingleMainPhone((Phone) entity))
FAILURE: Build failed with an exception.
But when you hot-deploy on the running application, you cannot see it, because the compilation is done by the application itself. You will see the cause only in the error dialog details when you open the screen.