How do I catch an Ajax query post error?

Since jQuery 1.5 you can use the deferred objects mechanism:

$.post('some.php', {name: 'John'})
    .done(function(msg){  })
    .fail(function(xhr, status, error) {
        // error handling
    });

Another way is using .ajax:

$.ajax({
  type: "POST",
  url: "some.php",
  data: "name=John&location=Boston",
  success: function(msg){
        alert( "Data Saved: " + msg );
  },
  error: function(XMLHttpRequest, textStatus, errorThrown) {
     alert("some error");
  }
});