You may find that an article doesn't have an Altmetric score, that is, the score is zero. Altmetric themselves say “most articles will score zero”.
The exact proportion of articles with an Altmetric score varies from journal to journal, but a mid-tier publication might expect 30 - 40% of the papers that it publishes to be mentioned at least once, with the rate dropping rapidly for smaller, niche publications. So the lack of a score should be understood in this context.
If an article doesn't have an Altmetric score - does this matter? Well, you should remember that Altmetric is aiming to track the “social web”, with the heaviest weight given to online news and blogs. So really what the score (or lack of) means will depend on the area of research and whether it is the type of research you would expect to have this kind of attention. Some research will obviously more easily create a 'social buzz'.
Like any metric, the scores have their limitations, for example, Altmetric only collects data about articles from specific supported publishers / repositories. Also, if the article was published before July 2011, Altmetric will have missed any transient mentions of it, tweets in particular. As such, its score won't be accurate, and will represent a lower bound of the attention received.
The Altmetric score cannot tell you about: the quality of the paper or the quality of the researchers or the whole story...
If you are a Dundee researcher and would like to maximise your score - see: Ensure your articles are tracked and 5 tips for improving your article’s Altmetric score.