I installed GL-1.5 quite easily (thanks, developers!) and found no edit icon in static pages in the center block (when displaying the home page of my site with the default Professional theme), though I logged in as admin.
After doing a little search through the code, I think this has something to do with geeklog/plugins/staticpages/templates/centerblock.thtml, which doesn't contain {edit_icon} template var. After I added {edit_icon} to the template file, edit icon shows itself as in GL-1.4.1.
So I suggest changing centerblock.thtml like:
{content}
<p class="alignright">{edit_icon}</p>
So I suggest changing centerblock.thtml like:
{content}
<p class="alignright">{edit_icon}</p>