Well, yes it can. Sex is a means of communication. And just like with other forms of communication, it needs to be done in respect. When this mutual respect is there, during sex, you can open up to one another, and be at your most vulnerable. This will facilitate communication on a verbal level too later on, which will enable a more problem solving setting.

Sex can also be a stress reliever, and in that way it can also solve prolems.

And besides all that, sex also releases specific hormones, which makes people open up and attach more to one another, which can also be the basis for some problem solving.

And as an extreme example, sex can be used in many 'not so nice' ways to fix problems of totally different types, because sex is something that is always in demand.

So it depends on the type of problems. It will not fix your broken leg, or cure the flu you're suffering from, but it can fix your relational problems, or even get your flat tyre replaced.