Here's a variation on Sjoerd's solution.
The main difference is to use a docked cell instead of a popup dialog. The cell has a link to the new post, as well as a button that will clear the docked cell to the previous state.
The other difference is to use the question ID instead of the title for determining new posts. I know that titles get edited sometimes, so this trigger as a new post in that case.
storedTitle = "";
storedID = 0;
mySOWatchTask =
CreateScheduledTask[{lastTitle,
lastID} = {"title",
"question_id"} /. ("questions" /.
Import["http://api.stackoverflow.com/1.1/questions?key=
QEpjCjsXYE6s_kZEkFr4Lw&page=1&pagesize=1&sort=creation&
tagged= mathematica", "JSON"])[[1]];
If[lastID != storedID,
storedTitle = lastTitle;
storedID = lastID;
SetOptions[$FrontEndSession,
DockedCells ->
Cell[BoxData[
ToBoxes[Style[
With[{dock = Options[$FrontEndSession, DockedCells]},
Grid[{{Button[Style["[CircleTimes]", 16],
SetOptions[$FrontEndSession, dock],
Appearance -> None], "New StackOverflow question: ",
Hyperlink[lastTitle,
"http://stackoverflow.com/questions/" <>
ToString[lastID]]}},
Alignment -> {{Left, Left, Left}},
ItemSize -> {{2, 14, Scaled[0.7]}}]],
FontFamily -> "Times"]]], "DockedCell",
Background -> Orange]]; EmitSound[Sound[SoundNote[]]]];, 60];
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