'this raises a problem' is correct and usable in written English.
You can use it to introduce a difficulty or obstacle that needs to be addressed. For example, "This raises a problem for conservation efforts: how to protect endangered species from poachers."
Design has taken on its own life, and this raises a problem often encountered in consumer culture.
But this raises a problem, and not just for those of us who were educated in the religious tradition, with parents who did not question the idea of God, and who still wistfully cling to the idea that there are things that are right, and things that are wrong, and that this rightness or wrongness might not be explained only by subtle sociobiological pressures over evolutionary history.
It seems that Democritus did not properly distinguish between the thesis of the physical uncuttability of atoms and that of their conceptual indivisibility: this raises a problem about how atoms can have parts, as evidenced by their variations in shape or their ability to compose a magnitude, touching one another in a series on different sides.
This raised a problem with the account of the science of demonstration Ockham inherited from Grosseteste.
But this arrangement raises a problem for the hemoglobin, the protein of red blood cells that takes on oxygen in the lungs and delivers it in the tissues.
Nevertheless, this theory raises a problem.
This raises a deep problem: Why should all human beings have this built-in facility for reading when writing is a relatively recent cultural invention?
This raises a potential problem when teaching science in high schools.
This raises a serious problem for the one-name-one-thing view.
This raises a central problem for resentment as a moral sentiment or passion: unless kept strictly within bounds it devolves into revenge and conflicts with benevolence and virtue.
This raises a different problem, noticed by Leibniz: because the conditions for the will choosing in accordance with the judgment are exactly the same as when it refrains from choosing, there is no explanation for why it does one rather than the other, in violation of the principle of sufficient reason (L 4.1, W 4.612; L 5.14, W4.634).
