As for logging into a course if the course title is not underlined and thus not an inutitive link to enter the course. Add a link to the course page (e.g. www.thesite/moodle/course/view.php?id=20) , call it login, enter course, etc., in the course description to make things more clear of what they need to do to enter their course.
For the generic login link. Add a login link (e.g. www.thesite/moodle/login/index.php) in the "Main Menu" section of the home page. This is a more intuitive "menu" like place for people to look as opposed to the upper right hand corner.
But I think there are some moodlers working on making the course description section on the moodle homepage more "customizable" and this might help things.