As a student I am not familiar with acceptance testing mostly because it involves a client. With acceptance testing, the program is given to the business or client and the client makes sure all of their specifications were met. This is done throughout the development process, not just once the program is complete.
This is a great way to test but there are some issues. One of the biggest ones is communication, because the program is handed off from the client to the tester to the developer, not specifically in that order, communication is often lost. All three often do not work together but just pass off code or specifications. Another issue is exposure of the program to the client. This can lead to the client thinking they know how to fix issues or how to develop code. There should be a clear line that the client should stick to their business and the developers do their jobs.
After learning about acceptance testing these are only a couple of the many issues out there, but I thought they were some of the most important.
http://www.softwaretestingmagazine.com/knowledge/problems-acceptance-testing-can-cause/
Software Testing 