I work with a wildlife rescue and during the spring intern of rescued babies this little gal came into my care. She's a goldfinch and I got her just before Halloween. I am unsure of her age but suspected she was around 18 days old or so when I got her.
Unfortunately due to local circumstances she cannot be released back into the wild so she will be living with me. I know in most countries it is illegal to keep wild goldfinches, but I live in New Zealand where it is legal to keep rescued ones.
Here is her picture when I first got her:

Her diet is soaked high protein kitten biscuits mixed with Roundybush Formula 3, Conditioning and Rearing Bird Softfood, and egg. She's been eating that regularly.
Here is a picture of her about a week after I got her:

Two weeks after:

Due to her messy feeding she's looking a bit rough for wear as she's missing some feathers round her crop area. She's a mess all the time and despite trying to clean her constantly she always finds a way to get food on herself!
This is her today, possibly 37 days old (right after a feed and before cleaning):


She's been flying around the house (It's bird safe) and made herself right at home. She's been foraging for food and trying out seeds, fruit and vege and pellet crumble, but has yet to stop screaming for her regular soft food around 4 times a day. Lately though despite her crying for food, when it is offered she seem's to want it, but not want it. She shakes her wings and get's excited but has stopped opening her mouth. So feeding her wet food is getting more difficult.
From what I can find (very little) goldfinches take longer to wean than other birds, but I suspect she should be weaned by now. I've tried holding off feeding her (letting her screech for an extra hour or so depending) and keeping a variety of food and seed available in all the areas she hangs out in (she mostly only goes in her cage at night, where there is always food and water available).
She's yet to try regular water or even to bathe herself, even though I keep a safe dish of water out for her to try.
So does anyone have any ideas on how I can help wean her/know if she's ready?