The great Apostle of the rosary St. Louis Maria de Montfort spoke in his book ‘The Secret of the Rosary’ about two mistakes that Catholics make when they pray the rosary.
St. Louis de Montfort said “whenever you say the Rosary, be sure to ask for some special grace or virtue, or strength to overcome some sin. Secondly he said that many Catholics simply want to get over with their rosary as soon as possible and fail to ask for any intentions at all.
So you see that especially for those who have pledged to pray the rosary every day, sometimes we see it as a burden and want to get over with it quickly and in doing so we do not even ask for any intentions when we pray.
You should always have an intention when you pray the rosary and even when you think that you have nothing to ask, you can pray for someone else or best your intentions could be ‘thanksgiving’. Secondly you should always ask for grace or virtues when you pray the rosary. It could be grace to live a holy life, grace to be a better Christian, grace to overcome sin, you could ask for the grace to be able to imitate one of the virtues of the Blessed Virgin Mary.
St. Louis Maria de Montfort identifies the ten principal virtues of the Blessed Virgin Mary as Profound humility, Lively faith, Blind obedience, Continual prayer, Universal mortification, Divine purity, Ardent charity, Heroic patience, Angelic sweetness and Divine wisdom so in praying your rosary, you can be asking for the grace to imitate one of these great virtues of the Blessed Virgin Mary.