He swore that he would stop watching movies, then he watched a movie by mistake. Does he have to offer expiation, and how can he stop watching movies?

Praise be to Allah.

Firstly: 

Movies are not free of a number of haraam things, such as women displaying their adornments, music, and so on. We have previously discussed the ruling on all movies, including a number of the haraam things they contain, in the answers to several questions. See the answers to questions no. 72204, 85232, 125535 and 114707. 

If the movies are indecent or permissive, then the prohibition on watching them is even more emphatic. 

For more information please see the answer to question no. 12301. 

Secondly: 

Your vow not to watch movies includes all kinds of movies, so long as you did not intend anything specific. 

Based on that, it is not permissible for you to watch any movie and if you go against that then you have to offer expiation for breaking an oath (kafaarat yameen). 

The sin that is involved in watching movies applies whether one vowed not to watch them or not. 

But, with regard to the expiation for breaking an oath, this expiation is not required if at the time of watching it one had forgotten the oath. 

To find out more about the expiation for breaking an oath and what it entails, see the answers to questions no. 9985 and 9943. 

Ibn Qudaamah (may Allah have mercy on him) said: 

Whoever swears that he will not do something, then he does it by mistake (because he forgot) does not have to offer expiation for it. A number of scholars narrated this from Ahmad. This applies except in the case of divorce (talaaq) and manumission, in which case it is regarded as breaking the oath. This seems to be the view of the madhhab and it is the view favoured by al-Khallaal and his companion. It is also the view of Abu ‘Ubayd and of al-Shaafa‘i, because of the words of Allah (interpretation of the meaning): “And there is no sin on you concerning that in which you made a mistake, except in regard to what your hearts deliberately intend” [al-Ahzaab 33:5]. And the Prophet (blessings and peace of Allah be upon him) said: “Allah has forgiven my ummah for mistakes, what they forget and what they are forced to do.” And because he did not intend to go against it, so he has not broken his vow. This is like one who is asleep or one who is insane. End quote. 

Al-Mughni Sharh Mukhtasar al-Khuraqi, 9/391. 

Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) said: 

If someone says, By Allah, I will not read this book today, then he forgets and reads it – he does not have to do anything, because he forgot. But if he has no excuse (for breaking his oath), such as being compelled or forgetting, then he has to stop as soon as that excuse no longer applies, otherwise he has broken his oath. End quote.

Al-Sharh al-Mumti‘ ‘ala Zaad al-Mustaqni‘, 15/137-138 

See also the answer to question no. 42334 

Thirdly: 

With regard to ways of stopping watching movies, you can achieve that by means of things that have been mentioned by the scholars and educators. For details on that please see the answer to question no. 159366. 

We ask Allah to help you to do that which He loves and which pleases Him. 

And Allah knows best.