My dad wanted me to watch this, too. As something resembling a semi professional singer/actor, I don't get what the big deal is. They were mugging for the camera when they rolled their eyes at her age/comments about "one side of me". The "rude audience skank" hardly represents an entire audience. And what Simon said afterward is obviously a play on the fact they thought she was going to suck, not him actually going "Wow, I knew you were great all along".
So a 47 year old can sing "I Dreamed a Dream" decently. She has a nice voice in a certain range, but she's not THAT good overall. Go YouTube that song, and listen to it several times. That song requires power in certain areas to excel at, and I'm just not seeing it from her performance. A lot of what many seem to think is pure "talent" is the microphone amplifying what appears to be a fairly weak voice. It's possible she's nervous, but I don't think so. She's struggling like hell to hold her notes in most important spots, and as has been pointed out, her vibrato is pretty awkward. It's decent, it's a nice moment for her to be sure, but that's not a breathtaking performance on any level.