What is the meaning of "dhammā" in the context of the four satipaṭṭhāna?
I think the following perspective on all four satipatthanas will help in understanding the  meaning of the fourth one. The four satipatthanas are supposed to counter the four vipallasas (perversions) which are: permanence, happiness, self, and beauty. So, mindfulness of the body counters the beauty perversion; mindfulness of feelings (and the fact that all vedanas are included in dukkha) counters the happiness perversion; mindfulness of mind (which is anicca) counters the permanence perversion; and, finally, mindfulness of the dhammas counters the self (atta) perversion. Thus, one reviews dhammas to realize anatta. To view four perversions would be inappropriate attention (ayoniso-manasikara), but the four satipatthanas, would be training in appropriate attention (yoniso-manasikara).

So, overall, I think the meaning of dhamma in this context is exactly what they are: analytical properties of experience, ultimate phenomena, and everything else that apply to dhammas (mind objects, matikas, dhamma lists, etc).