Is there a problem of intentionality? That depends what intentionality is. Let's accept the following definition, for the sake of argument.
(1) Intentionality: the existence of some thoughts depends on the existence of external objects
Is that a problem? Yes, and for two reasons.
First, a psychological reason. It is intuitive that thoughts, which are part of our mind, don't depend on the existence of objects external to our mind. If they did, we would automatically know whether there objects corresponding to them are not. For example, I can wonder whether the Antichrist exists, and I can have thoughts about the Antichrist. Or at least it seems to me that I can think about the Antichrist. And if it seems to me that I think p, that I do think that p (this is the 'Cartesian intuition' - I cannot be mistaken about the existence and nature of my own thoughts). But if a thought about the Antichrist requires that the Antichrist exists, and if I am thinking about the Antichrist, then the Antichrist exists. But that is absurd, for my thought is to question whether the Antichrist exists at all. Therefore my thought about the Antichrist does not require that the Antichrist exists.
Second, a psycho-physical reason. It seems plausible that the existence and nature of our thoughts depends upon the existence and nature of certain biological processes (i.e. in the brain). But the existence and nature of biological processes is in theory independent of things that exist outside. Therefore the existence and nature of our thoughts is independent of what exists outside.
Therefore there is a problem of intentionality. Many philosophers have tackled the problem by questioning whether we have 'Cartesian intuitions', or by theories of mind that are consistent with (1). I shall not be approaching the problem this way. The intentionality thesis, as expressed by proposition (1), seems to me fundamentally false. Instead, I shall be making a series of posts looking at the arguments for (1). More later.