Definitions can go wrong in various ways; for convenience one can refer to these as fallacies of definition (by analogy with the logical fallacies). This is a typical sort of list found in texts used in college logic courses.
Circularity: defining with a synonym. A definition is no good if it simply gives a one-word synonym. For example, suppose we define the word 'virtue'--an important word in ethics--just using the word 'excellence'. It might be perfectly true that all virtues are excellences and all excellences are virtues (that was perhaps an ancient Greek view; see arete), but the word 'excellence' by itself is not a good definition of "virtue," in philosophy. One can always simply ask, "But what does 'excellence' mean?" Surely, if one has a basic confusion about what 'virtue' means, then one will also have a basic philosophical confusion about what 'excellence' means. So it will not do to define one simply by stating the other.
Circularity: defining with a near synonym. A definition is no good if it uses a very near synonym in the definition. For example, suppose we define 'beautiful' as 'possessing aesthetic value'. The words 'beautiful' and 'aesthetic' are very nearly the same in meaning; so if anyone is deeply confused or curious about beauty, then she is of course going to be confused or curious about the aesthetic. The question is what general characteristics are possessed by all beautiful objects, or all objects that have aesthetic value.
There is a general name for the first two sorts of error: circular definition. A circular definition is somewhat similar to a question-begging argument: neither offers us enlightenment about the thing we wanted to be enlightened about.
Over-broad definitions. Definitions can be too broad. Suppose we define 'bachelor' as 'unmarried male'. On first glance this might look all right, but it applies to a lot of things, for example, male dogs, and male babies, that, needless to say, are not bachelors. A definition is too broad if it applies to things that are not part of the extension of the word defined.
Over-narrow definitions. Definitions can be too narrow. That is, they can exclude some things that they should apply to; they fail to describe some members of the word's extension. Here is an example of a narrow definition: 'piece of furniture' means 'object used to sit on'. Of course, some pieces of furniture are not used to sit on; for example, we put objects on them (like tables) or we put our feet on them (like footstools), and so forth. So even though some pieces of furniture are objects that are used to sit on, not all furniture is used to sit on. We need a broader definition: we might add other qualifying characteristics, like 'used to put feet up on' or 'used to put household objects on', for example. That would make the extension of the definition bigger--that is, the definition would apply to more things, and more of the things that we use the word 'furniture' to describe. We might also choose to entirely rewrite the definition, since laundry lists of characteristics strung together by 'or' are generally regarded by philosophers as not describing a unitary concept.
Obscurity. Definitions can go wrong by using ambiguous, obscure, or figurative language. Suppose we defined 'love' as 'the insensible quivering of the soul'. This is useless. Given a definition like this, one has the right to ask: but what is the insensible quivering of the soul? How would we recognize it? Is Johnny's soul insensibly quivering right now? And so on. Definitions should be stated in plain, straightforward language that can be understood by the people to whom one is giving the definition. See jargon.