One difference I notice is that my visual studio debugging environment appends /default.aspx to the end of the url, whereas when I open directly from the browser it doesn't append that. When the url ends with default.aspx I cannot go into edit mode from the home page, even if I type it in from the browser. But if I change to another page, other than the home page, then I can go into edit mode and I can lock in edit mode to stay that way, then I can go back to the home page and edit the page that way.