A quick braindump:
Profile are a great way of simplifying the interface and provide more focussed forms, but some of the goodies of the normal edit form are gone. For instance, the employer isn't anymore an autocomplete field. luckily, with the REST interface and a jquery autocomplete plugin, that's a few lines to add to make it work:
add on the templates/CRM/Profile/Form/Edit.tpl
{if $session->get('userID') > 0} {literal} jQuery(document).ready(function($) {