The two-dimensional surface shear viscosity, eta, of fatty acid monolayers of different chain lengths, measured using a simple magnetic needle viscometer, strongly correlates with the molecular organization in condensed phases and the absolute temperature. eta can increase by orders of magnitude at phase boundaries associated with tilted to untilted molecular order, providing the underlying order is semicrystalline. Hence, untilted, long-range ordered CS phases are the most viscous films. However, despite being untilted, the LS rotator phase is less viscous than certain laterally ordered tilted phases, suggesting a decrease of the van der Waals interactions due to molecular rotation. In certain regions of the L2 phase, eta reaches a maximum before the L2-LS transition, an anomalous behavior correlated with the change in the lattice symmetry of the headgroup. Surface shear viscosity, even when measured with a macroscopic probe, is particularly sensitive to the microscopic organization of monolayers.