Langmuir-Blodgett deposition is a popular route to produce thin films of graphene oxide for applications such as transparent conductors and biosensors. Unfortunately, film morphologies vary from sample to sample, often with undesirable characteristics such as folded sheets and patchwise depositions. In conventional Langmuir-Blodgett deposition of graphene oxide, alcohol (typically methanol) is used to spread the graphene oxide sheets onto an air-water interface before deposition onto substrates. Here we show that methanol gives rise to Marangoni flow, which fundamentally limits control over Langmuir-Blodgett depositions of graphene oxide. We directly identified the presence of Marangoni flow by using photography, and we evaluated depositions with atomic force microscopy and scanning electron microscopy. The disruptive effect of Marangoni flow was demonstrated by comparing conventional Langmuir-Blodgett depositions to depositions where Marangoni flow was suppressed by a surfactant. Because methanol is the standard spreading solvent for conventional Langmuir-Blodgett deposition of graphene oxide, Marangoni flow is a general problem and may partly explain the wide variety of undesirable film morphologies reported in the literature.