Take the following example (with appropriate imports):

public static void main(String[] args) {
        List<Number> x = new ArrayList<>();
        x.add("asdf");
}

The error message say:

error: no suitable method found for add(String)
        x.add("asdf");
    method List.add(int,Number) is not applicable
      (actual and formal argument lists differ in length)
    method List.add(Number) is not applicable
      (actual argument String cannot be converted to Number by method invocation conversion)

We display this message on different places in the IDE:

1. Tooltip when you hoover with mouse over the underlined text
2. If you move caret to the affected area it is shown
  a. In the status message
  b. after hitting Alt-Enter it is shown in place in the editor
3. In the output window if you hit compile
4. In the Window --> Action Items view

The error message mentions several classes and methods - at least on some places we can provide hyperlink either to source or to JavaDoc.

Also the error message has 2 parts: summary and details. On some places we might consider showing only the summary (e.g. in 4.) on some places we might split the message and show the details only after the user e.g. clicks "Details".