This paper provides new theoretical insights into the properties of direct detection differential phase-shift keying (DPSK) signals impaired by coherent and incoherent crosstalk. Coherent crosstalk is due to multiple replicas originated while a data signal is routed through an optical network, whereas the source of incoherent crosstalk resides on the interference from other DPSK signals. A special emphasize has been put on modeling the multipath coherent crosstalk, with analytical expressions being derived and presented for both the moment generating function of the decision variable and the average error probability. A rigorous analysis, capable of dealing with arbitrary filtering, is also presented, which is used afterwards to assess the accuracy of the analytical formulas. A detailed comparison with incoherent crosstalk is also performed. Using also an exact treatment for this type of crosstalk it is shown that for low OSNR penalties the coherent crosstalk leads, in some circumstances, to slightly worse results than the incoherent one, but this situation is reversed when the total crosstalk level and the number of interferers increase.