I know there's an appeals process but the whole secrecy element makes it hard for this to be effective for those who really have been short-changed by the system. The ones that haven't aren't going to gain anything by a more open system, the judgement should still hold up for them. However, if, as I and many others believe, while NOT being in the parents position (so not having the same emotional bias, there are quite a few wrongful decisions made, greater transparency would help to change those.
There are many imperfect judges, lawyers and social workers, but generally having their work scrutinised by anyone who wants to helps keep mistakes to a minimum and justice up. Take away that balance and mistakes/bad judgements can't be rectified.
Also, look at it from the other angle, what if mistakes are being made that leave children with unfit parents? Surely more scrutiny can help there too.
Plus it helps to get advice from more than one place, just look at MN for a case in point, people come on here every day for advice that technically they should get from a professional but there's solidarity in numbers, sharing a problem with 'outsiders' often helps to solve it or point out any errors.
For me it boils down to not being able to think of one single instance where having a secretive court leads to better outcomes than a more open one. As I write that I can't help thinking of Guantanamo Bay - courts may be out to do the right thing but it doesn't mean they're going about it the right way and in the end only the public can judge because we are the people it affects, so if the public can't check whether a system is working or not then that, to me, sounds dangerous whether mistakes are being made or not.