Two-point fat-water separation methods are increasingly being used for chest and abdominal MRI and have recently been introduced for use in MR angiography of the lower extremities. With these methods, flowing spins can accumulate unintended phase shifts between the echo times. The purpose of this study is to demonstrate that these phase shifts can lead to inaccurate signals in the water and fat images. In vitro experiments were conducted at 1.5T and 3.0T using a stenosis-mimicking phantom and a computer-controlled pump to image a range of physiologically relevant velocities. In the phantom images acquired using bipolar readout gradients, fat-water signal inaccuracies were visible in regions of flow, with increasing severity as the flow rate was increased. Additionally, similar effects were observed in regions of high flow in clinical chest and liver exams. In the phantom images, the effect was eliminated by using a dual-pass method without bipolar readout gradients. When using fat-water separation methods with bipolar readout gradients, phase shifts caused by the motion of spins can lead to signal inaccuracies in the fat and water images. These artifacts can be mitigated by using approaches that do not use bipolar readout gradients.