I'm a Chinese national with a type F Belgian residence card ("familielid van een burger van de Unie"). According to the EU law, it seems that I don't need a visa to enter Ireland as a tourist. Will I encounter problems at immigration because my residence permit is in Dutch?
The language shouldn't in itself be a source of trouble -- border guards will have access to documentation about how the relevant residence permits of other member states look.
Note, though, that your rights under the Directive only apply when you're traveling with (or traveling to join) the union citizen in question. If you're traveling on your own you can be required to have a visa.