The Multiphysics Object Oriented Simulation Environment (MOOSE) is a code package that couples a variety of physics modules, allowing for highly accessible multiphysics simulations. The physics modules include a finite-element Navier-Stokes (N-S) module that is designed to solve laminar fluid dynamics problems. The usage of this module in multiple recent studies coupled with the growing interest in MOOSE for usage in non-LWR safety studies by the Nuclear Regulatory Commission (NRC) prompted the authors to investigate the computational fluid dynamics (CFD) capabilities of MOOSE. A 2D flow past a round cylinder scenario is simulated in the MOOSE environment to investigate the effectiveness of the N-S module. The simulation assumed an unsteady laminar flow with a Reynolds number of 200, where the unsteadiness in the vortex street is captured using a Euler-implicit time-integration scheme. To verify the results from MOOSE, a similar simulation is conducted using the well-utilized OpenFOAM finite volume code, and the velocity profiles of both transient simulations are compared. Grid and input sensitivity studies are conducted in MOOSE to quantify the numerical and input errors, respectively. The numerical and input errors are also visualized with contour plots in order to qualitatively understand the evolution of the errors across time and space. Results show that MOOSE struggles with capturing the instabilities in the flow, as it takes more than 20 seconds before a vortex street is observed. Excellent agreement in the velocities is seen between MOOSE and OpenFOAM upstream of the cylinder, but huge discrepancies can be seen where instabilities are expected around the cylinder and upstream of it. The discrepancies become more severe as the transient simulations progress in time. The numerical error is most prominent in the wake of the cylinder and around the boundaries of the channel. The input errors are also prominent in the wake but are most prominent around the cylinder walls. The results demonstrate the difficulties faced by the N-S module in MOOSE when it comes to simulating unsteady flow and prompts questions about the effectiveness of finite element CFD solvers.