Lots of kinds of noise and artifacts may appear on MRI images. I don’t think there is any simulator readily available as a Slicer module. If you want to have something simple, such as simulating Rician Noise then you can easily add it using a few lines of Python code in Slicer (see example here). If you want to do generate more sophisticated noise or artifacts then you try various MRI simulators (there must be ones implemented in Python that you can use directly in Slicer).
To add simulated distortion (e.g., due to soft-tissue motion) then a simple method is to create a warping transform by prescribing displacements at selected control points. See complete example here. Hardening of the transform using this example script does not work in latest Slicer Preview Release, but I’ve already fixed the issue and it will work in tomorrow’s version.