Instead of showing the errors you can implement the Application_Error function if you are using a single web project, or you can override the OnError event if you are using a custom base Page class. In there you can send an email to yourself containing the detailed error info, or log it in the event viewer. Below is an example:
protected override void OnError(EventArgs e)
{
try
{
Exception exMyError = Server.GetLastError();
exMyError = exMyError.GetBaseException();
//SEND THE EMAIL OR LOG INTO EVENT VIEWER
}
catch(Exception)
{
}
finally
{
//SEND THEM TO THE ERROR PAGE
}
base.OnError (e);
}