Many a time I memorize Ayahs of the Noble Qur'an but I forget them after a while. Moreover, when reading a certain Ayah, I doubt whether my reading is correct or not. Later, it turns out to be incorrect. Please, advise. May Allah guide you!
It is prescribed for you, my brother, to exert effort in memorizing what you can of Allah's Book and to recite before some good Sheikhs at school, in mosque, or at home. You should do this regularly so as to correct your recitation, because the Prophet (peace be upon him) said: The best among you (Muslims) are those who learn the Qur'an and teach it. (narrated by AlBukhari(may Allah be merciful with him) in his Sahih). Thus, the best among people are the people of the Qur'an who learn and teach it to people and put it into action.
The Prophet (peace be upon him) said to some of his Companions: Which of you would like to go early in the morning every day to Buthan (a valley in Madinah) and return from it with two largehumped shecamels, without committing a sin or severing the ties of kinship? They replied, "O Messenger of Allah! We (all) would like that!" He (peace be upon) said: "If any of you go to the mosque and learn or recite two Ayahs from the Book of Allah, this is better for you than two shecamels, and three (Ayahs) are better than three (shecamels), and four (Ayahs) are better than four (shecamels). And the number (of Ayahs recited in total) are better than the same number of camels." or as the Prophet (peace be upon him) said.
This shows the virtue of learning the Noble Qur'an. Dear brother, you should learn the Noble Qur'an at the hand of Sheikhs wellknown for their proficiency in reciting the Noble Qur'an to receive the benefit and correct your recitation.
As for your forgetfulness, there is no harm on you regarding this. Every one is liable to forget as the Prophet (peace be upon him) said: I am a human being like you and liable to forget like you. Once hearing someone reciting the Noble Qur'an, the Prophet (peace be upon him) said: May Allah show mercy to so and so; he has reminded me of such and such an Ayah which I had missed. i.e. "I forgot it". The meaning is that one may forget some Ayahs and remember them later or some other persons may remind him. It is better that one should say, "I have been made to forget," because it is reported that the Prophet (peace be upon him) said: "None of you should say, 'I forgot suchandsuch an Ayah', but he has been made to forget." This means that Satan made him forget. As for the Hadith:
"No man recites the Qur'an, then forgets it but will meet Allah on the Day of Judgment in a maimed condition (or emptyhanded, or with no excuse)", this is a weak Hadith according to the view of Scholars and was not related from the Prophet (peace be upon him). Forgetfulness is neither out of one's choice nor capacity to recover from it. This means that it is ordained for you to memorize what you can of Allah's (Glorified and Exalted be He) Book and to do that regularly before Sheikhs who are professional in recitation to correct your mistakes.
May Allah grant you success and make matters easy for you!