What are the features of a well-written puzzle?

When making a new puzzle, the average person is usually faced with a hard problem of guaranteeing quality.

I want to know some key points and ideas, for beginners and experts alike, to keep in mind when creating their puzzle, because a good puzzle must be well-polished. What are some features of good puzzles that apply broadly to a wide range of types of puzzles? I would imagine careful management of difficulty - something like the requirement of play-testing - would be an aspect to consider, for example.

Answerers are encouraged (but not required) to provide examples of features, common mistakes, and ways to improve a puzzle.

Answer

From my experience as corrector of text puzzles on a Russian puzzle site 3 features are required for a puzzle to be liked by solvers (in order of importance): motivate, be correct, do not be straightforward.

1. 
   

   It is Interesting. It must have something unusual. This is clearly the most important, if a reader does not expect to to get a new knowledge and experience he won't even try to solve it most probably. For example, x^2-2x+1=0 would not be a puzzle at all, just because it is standard quadratic equation.
   
   So, what can be unusual about a puzzle?
   1.1. Unexpected, beautiful fact to prove. For example, draw a shape which can be cut both on 3 and 4 equal triangles. Or, a puzzle about passenger, which comes to a bus stop at a random moment and most often meet his bus, that goes into wrong direction.
   1.2. It's answer seem to be impossible. For example, a puzzle which asks how to measure diagonal of a brick in one measurement with solid ruler, or prisoners problem.
   1.3. It's answer can seem to be too obvious (but this obvious answer must be wrong of course). For example, can whites win in this position?.
   1.4. It can be about unusual properties of well know objects. For example, "Is it possible in a Cartesian coordinate system to position a regular tetrahedron so that all its vertices lie at the points with integer coordinates?".
   1.5. It can look too complex to solve (but one should know that it is a puzzle, not a practical question and it has found, simple solution). For example, ants on a stick puzzle.

   
   


2. 
   

   It's task is Easy to Read and Understand. At least, the understanding of the task must require much less time than the solution itself.
   To be like this it must be:
   
   2.1. complete. It must have all special information reader needs. And it must allow only one interpretation. But, note that there are well know facts, these don't have to be included in the formulation of the puzzle, and nobody can create a puzzle that can not be misunderstood.
   2.2. compact, any word you put in you must think though, you must ask yourself whether it is really needed there.
   2.3. tested. It must be read by several people, different people always see one thing differently, the author alone can't predict all problems.
   2.4. reading process should be pleasant. So you better check you spelling, structure and order of phrases. Also, it is always nice to find appropriate "interface" for the idea behind a puzzle, all puzzles can be formulated in a strict mathematical language, but if you find real-life situation, that fits your idea the puzzle would became much easier to remember and understand.

   
   


3. 
   

   It's Solution is Interesting. The solution should have a new idea behind it. It's very nice when it simple to understand and compact, but meanwhile is hard to find (not straightforward).