In Scala.js 0.6.26 the from JavaScript accessible method possiblyBroken throws an Exception when being called from JavaScript. A look in the compiled code shows, that it lacks the code for handling variable arguments that notBroken1 and notBroken2 have.

trait Foo {
  @JSExport def possiblyBroken(args: Int*): Unit = ???
}

class Foo2 {
  @JSExport def notBroken1(args: Int*): Unit = ???
}

@JSExportTopLevel("bar")
object Bar extends Foo2 with Foo {
  @JSExport def notBroken2(args: Int*): Unit = ???
}