Learn Spanish (Latin America): Ya había notado que el centavo tenía una marca en el reverso. - I had already noticed that the cent had a mark on the back.

We use tenía because we are describing an ongoing characteristic of the coin in the past. The coin having a mark wasn't a sudden, completed event; it was just a physical state that already existed when you noticed it.

Could I use me había dado cuenta de que instead of había notado que in this sentence?

Yes, they are almost perfectly interchangeable here. Darse cuenta de is a very common way to say to realize or to notice. Notar often emphasizes physically perceiving a detail, which fits perfectly for seeing a mark on a coin.

Why is the word for back reverso rather than espalda?

Reverso specifically refers to the reverse or flip side of a two-sided object, like a coin, medal, or page. Espalda is strictly used for an anatomical back, like a person's or an animal's back.

How does ya work with the past perfect tense here?

Ya means already. Combined with the past perfect or pluperfect (había notado), it simply emphasizes that this action was fully completed before some other past event happened in the speaker's overarching story.