I have made an application using Visual Studio LightSwitch 2011 (v1) running on Visual Studio 2010 Professional. It is a desktop application, and I use SQL Server Authentica
Check out Eric Erhardt's article. Here's a quote:
When your application fails to load data successfully, the screen will display a red X and the tool tip will say “Unable to load data. Please check your network connection and try loading again.”
A little known secret about LightSwitch is that the server has a Diagnostics subsystem integrated with ASP.NET tracing. LightSwitch’s Diagnostics subsystem is a lot more powerful than just telling you what exception was thrown when issuing a query. You can use it to trace through the actions that were requested of the server, and what steps the server took in response to each action. So even if things seem to be working, you can get more information about what your application was actually doing.
So you can enable diagnostics then open the trace at: your-lightswitch-application-address/trace.axd. You can then check the error details (screenshot taken from the blog article):

Another alternative way is to use Fiddler. It is also explained in the same article.