I might be insulting the sensitivities of my Ulster friends, but I never have understood why they are so crazy about this particular dictionary. Of course, it is in the old orthography, but it is a mistake to think that it would make the reading of, say, Seán Bán Mac Meanman or the Grianna brothers any easier: most unusual words found in them are included rather in the Ó Donaill dictionary than in Dinneen. So, it is a mistake to think that Dinneen covers Ulster Irish any better.
However, some of Dinneen's attempts to define Irish words do capture the essence of traditional usage better than Ó Donaill. Besides, Dinneen doesn't take it for granted that the dictionary user already understands Irish English (Ó Donaill does, a fact that leads to such hilarious "translations" as "pampooties" for "pampútaí" - forgetting that a Britsh, an American or, say, a Finnish reader, although familiar with standard English, does not always understand such Hiberno-Englishisms as "pampooties") and thus often adds explanations for the uninitiated. But Dinneen does not organise the dictionary articles very well, and often he is as vague as to be incomprehensible. And of course, today's most current meaning of a word isn't always the one that comes first, or even among the first, in Dinneen.
Dinneen's is an indispensable tool for a writer in Irish or a scholar doing research, but general learners should first of all get a copy of Ó Donaill. However, sooner or later you must get accustomed to the old orthography, and then you'll need Dinneen.