Intellectually speaking, the ‘problem of evil’ involves events such as boring afternoons, or getting bitten by an ant, or becoming a little chilly for a few seconds, or indeed, any suboptimal happening – such as being joyous but not completely, ultimately joyous, say – as part of a proof against the existence of a classical omni-God.
For, if God were omnipotent in the sense of being able to ‘snap his fingers’ and have any result occur, and if he were omnibenevolent, then it seems we would instead expect to be in a state of perpetual bliss (at least, immediately after we chose to be in one).
I think the proper conclusion to draw from these sorts of considerations is that there’s something wrong with our conception of God and the universe, if that’s what we think an omni-God entails.
That is, however God’s omnipotence and omnibenevolence is to be understood theologically, it works its way out as a process (see here for a tentative definition of process omnipotence, or here for more considerations on the classical philosophical conception of omnipotence), where it seems an integral part of that process is us learning and growing.
Methodically speaking, instead of starting from the supposition of a classical omni-God and therefore be instantly subject to an argument based on the ‘problem of evil’, one can rather begin with various experiences (which one can see in everyday Christian experiences, say), and then one can start to move towards various Christian conceptions of God’s attributes.
I.e., one can build-up a conception of God’s omnipotence (and so on), such that whatever it means, it is reflected in such-and-such events. If one does this, the ‘problem of evil’ has much less impact intellectually speaking – i.e., as an intellectual obstacle to Christianity. (This does not speak to the emotional component, although I think it begins to put it in a different context.)