This video shows that she has a relatively decent singing voice.
I Liked It Better When It Sucked: There's a faction out there that loved "Friday" because it was so horribly bad. It had terrible lyrics and overly autotuned vocals with generic pop music. However, "My Moment" was considered by by the public to be... listenable. It didn't have nearly the amount of cheesy fun the original had.
Misblamed: The lyrics and the abusive use of auto-tune were actually done by Ark Music Factory, the company that produced the music video, not Rebecca Black herself.
Though according to The Other Wiki, she did select this song out of a choice of two pre-written compositions, despite her mother's doubts. Rebecca's reason is that the unpicked track was about adult love, which she hadn't yet experienced at her age at that time.
Win the Crowd: After the reception "Friday" got, she could have easily become a Justin Bieber-esque figure, but her healthy amounts of Self-Deprecation as well as genuine improvement in later songs means she enjoys a quite good reputation now, with the remaining haters being more of a Vocal Minority.
The Woobie: After "Friday", the backlash hit so hard that people were bullying her in real life, with some going so far as to sending her death threats. She eventually turned this around by going on to donating the profits from the song to Japan's relief fund for the 2011 tsunami.