I was having this issue recently also but with the Attribute Inspector. I changed the click query to give me a tolerable extent by using the click query syntax from the "Related Records" sample under FeatureLayer samples. It seems as though the probability of actually clicking on an infinity small point is very low (A bit of humor there).
Here is the bit of code that I used to enable me to click a point and display the Attribute Inspector...
var tol:Number = myMap.extent.width / myMap.width * 5;
var x:Number = event.mapPoint.x;
var y:Number = event.mapPoint.y;
var queryExtent:Extent = new Extent(x - tol, y - tol, x + tol, y + tol);
var thisSelectionQuery:Query = new Query();
thisSelectionQuery.geometry = queryExtent;
myFeatureLayer.selectFeatures(thisSelectionQuery, FeatureLayer.SELECTION_NEW);
Maybe this will help