Learn Italian: Aggiungo qualche dettaglio senza che lui se ne accorga.

The phrase senza che (without) is a negative conjunction that always triggers the subjunctive. It introduces an event (him noticing) that hasn't happened or is being prevented, so it lives in the realm of subjectivity rather than fact.

What do the little words se and ne do in se ne accorga?

They belong to the verb accorgersene, which means "to realize" or "to notice something." The base verb is accorgersi (to notice). When you add ne (meaning "about it"), the reflexive pronoun si changes to se to make it easier to say.

The translation says "some details" (plural), so why is it qualche dettaglio (singular) in Italian?

The word qualche means "some" or "a few," but it is a special adjective that must always be followed by a singular noun. If you wanted to use the plural noun dettagli, you would need to use a different word for "some," like alcuni dettagli.

Why can't we just use the infinitive and say senza accorgersene?

You can only use senza plus the infinitive when the subject of both actions is the same person. Because "I" am doing the adding and "he" is the one not noticing, you have to split the sentence with senza che and use the subjunctive for the second person.