What looks problematic to you in this case?

The main problem Trinh is facing is that she is offering her students many ways in which she can be contacted by: university email, Blackboard email, and blog on Twitter.  Although Trinh cannot exactly set up “office hours”, she most definitely can set up parameters around how students can contact her. I would advise Trinh to have all messages from her students delivered to her university email account.  At first I thought it should be her Blackboard internal mail account, but as a student using Connect, I have to wait to login and check my internal mail to hear back from my instructors, which is an extra step for me.  If I could email my instructor from my gmail account and receive mail directly back to that account, it saves me more time, as I’m sure it would save my instructors more time.  I also recommend that Trinh set up a discussion specifically for issues that arise during the course.  Some of these issues include technical ones, not being able to access articles, or general course related questions.  With this forum set up, other students in the class can offer suggestions and help with the troubleshooting which will lessen Trinh’s email count.
Who are the stakeholders in this case, what has been done and what has not been done well by some of them?

If Trinh is spending more time on communication, then her students are suffering from not having more of an online presence from their teacher.  Trinh needs to focus more on her teaching presence: learners and teachers, and their interactions with each other and with content (Anderson, 2008a).  As Anderson (2008a) highlights that this interaction can take place within a community of inquiry, using a variety of net-based synchronous and asynchronous interactions, Trinh needs to evaluate how she is using these tools effectively.   It’s great that she is using a variety of multimedia educational artifacts, especially the streamlined live guest lectures.  Her students obviously appreciate this.
References:

Anderson, T. (2008a). Towards a theory of online learning. In T. Anderson & F. Elloumi (Eds.), Theory and practice of online learning. Edmonton AB: Athabasca University.