Rule: Mass nouns do not allow the plural or a(n).
Examples of errors:
Countability can be considered an inherent feature of nouns in English, just as grammatical gender is a feature of nouns in many other languages. Since such inherent features are generally unpredictable, the learner's ultimate resource must be native speakers or a dictionary, providing the dictionary includes such information. The analogy between gender and countability is not exact, however; gender is more inherent, so to speak (i.e. more predictable a feature) than countability, a fact which becomes apparent when we notice that monolingual dictionaries of French, German, etc. mark nouns for gender, but monolingual English dictionaries (except for learners' dictionaries such as Hornby 1963 and the Longman Dictionary of Contemporary English (1978)) do not mark nouns for countability. Countability in English, in other words, must be considered--by people who make dictionaries, at least--more accessible to native speaker intuition than gender in other languages.
One observation that may be of some help in predicting countabiiity is that abstract nouns tend to be mass (i.e. non-count) and concrete nouns count. The problem here is that, as we have already seen (cf. 1.1), the features of abstractness and concreteness are difficult to define. l@any nouns referring to tangible or concrete objects are mass (e.g. iron, butter, milk, hair in (5), toast in (11)), and many nouns referring to abstractions are or can be count (e.g. difficulty, worry, etc.)
A further complication to the problem of predicting countability is that a sizeable number of nouns can be used either as count or as mass nouns, with various degrees and shades of difference in meaning. Thus there is little or no difference between two coffees and two cups of coffee or have difficulties and have difficulty but a considerable difference between an iron (to press clothes with) and iron (the metal), competitions ('contests') and competition ('rivalry'--cf. (8)), a (mathematical) proof and proof in general (cf. (14)), a work (e.g. of art) and work meaning 'employment' (cf. (27)).
Co-occurrence restrictions often accompany a difference in meaning between the count and mass forms of the noun. For example, the preposition in usually precedes the mass noun condition meaning 'state of repair, health, or fitness'--cf. (4)--but under is used when the countable sense of 'prerequisite, restriction' is intended (e.g. under that condition/those conditions). It is worth noting, furthermore, that when there is a difference in meaning it tends to correlated with other semantic features. Thus the count meanings of nouns like iron, competition and condition seem to be both more concrete and more specific than the mass meanings. The same is true of impact meaning 'collision' versus 'effect'--cf. (3)--intervention meaning a specific act thereof, as opposed to intervention in general--cf. (9)--and troubles meaning 'problems' as opposed to 'difficulty'--cf. (12). The extent to which countability actually does correlate with these'other features is another question which calls for further investigation.