The two-dimensional surface shear viscosity, A, 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. A 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 L-2 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.