High In BlueJ, compiler error messages are shown in the info display at the bottom of the editor window. If you are using BlueJ via a screen-reader, they are impossible to read: you can't focus on the info panel, and when they appear they don't trigger the screen reader.
I think a suitable fix is to display the messages in a pop-up dialog (configurable via a setting). Although this might usually be thought irritating for most users, I think when you are using a screen-reader this is a reasonable solution (it pops up, reads the error message to you, then you hit space/enter to dismiss it and return to editing).