Nynaeve made a lot of serious errors in the chapter where she was raised to the shawl. It's always been difficult to keep up with Nynaeve's impulsive behaviour, and if she wasn't one of the strongest women on earth, I doubt she would have amounted to anything. The entire chapter displays how ridiculous her thought processes are.

The first mistake Nynaeve made was to break the rules of an exam. We all hate exams but only a moron challenges the rules on the day of the test. Most especially, Aes Sedai are renowned for how picky they can be with the test and how easily you can be put out of the Tower. Nynaeve starts by saying lines that aren't part of tradition. That alone could have ended the test for all she knew. All of us know how inane exam customs can be, but you follow them to reach the end point so that you can get on with your life.

After that Nynaeve carried on breaking rules. She was told not to run between the stars, and not to channel before she reached them, and she did both. After the test she initiates a saccharin speech about morality and the higher purpose that apparently silences all the Sitters (yeah right). The point of the test is to prove that the woman can remain calm and achieve a higher purpose in the face of extreme stress, which Nynaeve cannot do. The fact that Nynaeve wants to rescue children and other suffering people when she's exposed to them makes her a serious risk to a higher purpose. All the Shadow has to do to someone like Nynaeve is exploit a weakness like this, whereas a true Aes Sedai should technically be immune to this type of temptation. If Cyndane sees Nynaeve protecting Rand, all she needs to do is break Mat's legs and leave him bleeding at the bottom of the hill... Nynaeve would abandon all higher purposes and run to help him. Morally she can't be touched, but she's an utter failure in a test where the rules are explicitly stated prior to starting, and in the broader spectrum of life where a higher purpose really can be worth the death and suffering of others.

I've never thought that the test for Aes Sedai is bad. I actually think its ideal. Channeling under extreme stress is almost all that matters when someone who can wield something as deadly as the OP and is relied upon by the general populace, is raised. Consider a channeler who is in a palace and knows that she is about to be balefired and she needs to weave a gateway calmly to escape. What use is a woman who fumbles for the Source (as incidentally did happen)? What use is a woman who is disabled with fear when 100,000 Trollocs attack the manor house?

My only gripes with the test are the following...

1. It can be fatal. I find this unacceptable in a test. It should be based on illusion and have safeguards against serious injury or death.

2. Failure means being put out of the Tower. If a woman cannot channel under extreme stress, she needs to be moulded further until she can handle the situations. Its like being forbidden to drive forever if you fail your driving test. Some people just need that second chance.

Nynaeve rattled the saber because of her childish and belligerent attitude towards other Aes Sedai. She should have failed the test because she still cannot do what Cadsuane said of her in WH... learn to endure things even if it wasn't necessary. She breaks rules whenever she doesn't agree with them or reacts with hostility. She's an atypical Aes Sedai, which Rand likes, but ultimately I think she's erratic and unreliable as a channeler.