One of the "New Apostolic Reformation" beliefs that should be completely rejected is the ridiculous claim that there are apostles living today that are equivalent to the original (real) Apostles from the New Testament. Here's a quick little WWUTT video on this topic:

Further reading on the apostolic/prophetic office today:

Is God Restoring the Offices of Apostle and Prophet in the Church Today? 

Are There Prophets Today?

Are There Still Apostles Today?

Apostles and Prophets and the Foundation of the Church

Here are a LOT of additional resources about The New Apostolic Reformation (this is probably the most extensive compilation of NAR material anywhere on the internet): 

Has Your Church Fallen for the Lies of the N.A.R.?

The New Apostolic Reformation Cornucopia of False Doctrine, Dominionism, Charismania and Deception (there are 30 links here to extensive articles, interviews and programs-do your homework!)

The Bill Johnson Cornucopia of False Teaching, Bible-Twisting, and General Absurdity

The Rick Joyner Cornucopia of False Teaching, Bible-Twisting and and Overall Wackiness

The Charismatic Day of Infamy: June 28, 2008