This work considers the problem of diffusive molecular communication with mobile transmit and receive nanomachines. The optimal test is determined for symbol detection at the receiver nanomachine. To evaluate system performance, closed-form expressions are derived for the probabilities of detection and false alarm, probability of error, and capacity in the presence of impairments such as multi-source interference, inter-symbol interference, and counting errors. Simulation results are presented to corroborate the theoretical results derived and also, to yield insights into the performance of the system. Interestingly, it is shown that with a fixed molecule budget at the transmit nanomachine, the performance of mobile diffusive molecular communication can be significantly enhanced by allocating a larger fraction of the molecules for transmission in later time slots.