The new posts problem is typical of the read/mark read system on Vbulletin 3.5. In order to get around this, you must upgrade to vbulletin 3.6 whereby they have rewritten the system to give the administrator a few different options, including: don’t mark as read until member has actually read that specific thread 
P.S. Regardless of that Prof you should upgrade to 3.6. It’s pretty easy to upgrade. It makes things smoother and has many improvements.