Changing over to the AMD reference style seemed to work for me, but only if I use my local server copy of JS API 3.2. Here is how I am declaring my modules now:Old way:dojo.require("esri.map");
dojo.require("esri.tasks.query");
dojo.require("esri.tasks.identify");
dojo.addOnLoad(Init);
New way:require(["esri/map", "esri/tasks/query", "esri/tasks/identify"], Init());
I'm now running ArcGIS JS API 3.2, jQuery 1.9.1, and jQuery Mobile 1.3.0. The odd thing is that it will not work if I reference the 3.2 or 3.3 API on the Esri servers. It only works if I point to my local version.