A shaytaan Jinn may know some of the Qur'aan - he may even reach the level of hafidh of the Qur'aan - and he may have a great deal of knowledge about its virtues as well as other benefits related to the religion, but that doesn't mean that everything he says is worth listening too.
This hadeeth is recorded by an-Nasaa'ee in 'Aml al-Yawm wal-Laylah, al-Baghawee in Sharh as-Sunnah, al-Bukhaaree in at-Taareekh al-Kabeer, and Ibn Hibbaan in his Saheeh as well as others.
'Abdullaah Bin Ubayy narrated that his father had a storage space that contained some dates. He went into it and found that some were missing. So he kept watch over it. Later he found a beast that resembled an adolescent boy in it. He said, "So I gave him salaams, and he return salaams. So I said, 'What are you, a jinn or a human?' He said, 'Jinn.' I said, 'Show me your hand.' He showed me his hand, it was the hand of a dog with hair like a dog's. I said, 'Is this the way that jinns are?' He said, 'I know of the jinn what is worse than me.' Ubayy said to him, 'What made you do as you have?' He said, 'We have learned that you are a man who likes to give sadaqah, so we like to get some of your food.' Ubayy said, 'Is there something that will protect us from you?' He said, 'This Aayah, Aayat al-kursee. [Whoever says it in the evening, he will be protected from us until the morning, and whoever says it in the morning, he will be protected from us until the evening.]' The next day Ubayy went to the Prophet (sall Allahu alayhi wasallam) and informed him about what happened. He (sall Allahu alayhi wasallam) said, The evil one told the truth.
In Fath ul-Baaree (explanation of Saheeh al-Bukhaaree), Ibn Hajar mentioned a number of things that we can learn from in another hadith similar to the above hadith (hadith is in the comments) and of the virtues of Aayat ul-kursee, below are some of them;
1. That the shayateen are aware of what benefits a believer.
2. That wisdom may be taken from an evil person by which, although he did not benefit from it, one may benefit from it.
3. That a person can know something and not act upon it.
4. That a kaafir may believe some of what the believer believes, but that does not make him a believer.
5. That a liar may tell the truth.
6. That the shayateen usually lie.
7. That the jinn can appear in a form that can be seen by us.
8. That the jinn eat the food of humans.
9. That they may appear to humans.
10. That they speak the language of humans.
11. That they are thieves and tricksters.
12. That the jinn eat from food that Allaah's name has not been mentioned over.
13. That the thief's hand is not cut off in the case of starvation.
14. To accept one's excuse and forgiving him when you think he is telling the truth.
15. It demonstrates the Prophets' awareness (sall Allahu alayhi wasallam) of matters unseen.