Further reading has led me to try using ArgumentCaptors and the following works, although much more verbose than I would like.
ArgumentCaptor<String> argument = ArgumentCaptor.forClass(String.class);
verify(errors, atLeastOnce()).add(argument.capture(), any(ActionMessage.class));
List<String> values = argument.getAllValues();
assertTrue(values.contains("exception.message"));
assertTrue(values.contains("exception.detail"));