Lack of knowledge. This is very important, you should learn as much as possible before even thinking about buying anything. Books are expensive, but there are many other Articles and Informative Forums on-line packed with information and help.
Hard corals. These should be avoided until a full understanding of water chemistry and a confidence in maintaining these levels are achieved. These corals require more intense lighting requirements and feeding. Compatibility also creates issues too. As above really, learn about water chemistry, then research your coral selection carefully.
Expensive unnecessary equipment. As a newbie to Reef Keeping it is totally unnecessary to purchase Computers, Reactors, Top up devices, and any other fancy items that may arise. I say this because as a new Reef Keeper you need to understand and manage a Reef Aquarium. Having fancy computers and reactors will create loads of confusion. The same can be said about Calcium Reactors and so on, with issues such as overdosing.
Fancy expensive fish. Please walk before you run. There are loads of reasonably priced fish available, many colorful and rewarding too. Imagine how upset you would be to loose a expensive fish and think of the impact on the environment. Conservation is key to this hobby.
Overstocking. Don't rush out and buy everything you see and like, you will overload your aquarium and most likely kill your new livestock. Do it slowly and stock fish according to your aquarium size.
Overfeeding. This is something many get wrong. By overfeeding you are creating your livestock to produce more waste, Resulting in higher nitrates. Feed small amounts only when required.