Is it obligatory for a Muslim to bring to mind the three matters: love, fear, and hope, in their intention when performing acts of worship, or is it sufficient to bring them to mind after intending the act for the sake of Allah, and is there any problem with that?

The intention (niyyah) is the resolve to perform an act of worship seeking the countenance of Allah the Almighty. It involves bringing to mind the essence of the prayer, that it is obligatory, and specifying it, like the Dhuhr prayer, intending thereby to draw closer to Allah and seek His pleasure.

Therefore, what you do—the takbir (saying "Allahu Akbar") with the intention of performing the prayer you wish to offer for Allah the Almighty—is what is obligatory. It is not necessary to bring to mind love, fear, and hope in the intention, as these are actions of the heart that must be perfected and by which one journeys to Allah, even if they are not directly related to the obligatory intention.