Has radio astronomy ever been done on objects that appear very close to the Moon? Is this avoided? This answer to Which kinds of astronomical observations most need to avoid the Moon being up? mentions 


  For completeness - radio, mid-infrared and mm-wave observations are unaffected (unless the Moon is in the way!)


The Moon is of course opaque to all wavelengths used in astronomy, from very low frequency radio waves to gamma rays. So if the moon eclipses a target radio signals will be blocked.

But are there any more subtle or non-obvious effects? For example if a target is very close to the Moon but not covered by it, would that affect an observation in any way? 

Question: Is this routinely avoided out of an abundance of caution? On the other hand, has a lunar occultation of a radio source ever be leveraged in some way for a specific measurement? 

"Bonus points" for any anecdotes of strange results or confounding measurements in Radio Astronomy that turned out to be the result of not taking the position of the Moon in to consideration.
Yes, and lunar occultations have proved useful in several cases.

Hazard et al. 1963 used a lunar occultation to produce a high-resolution brightness profile of the now well-studied radio quasar 3C 273. Scheuer 1965 goes into a little bit of detail on general computations.

A slightly different tack was taken by Vedantham et al. 2015. They were attempting to create interferometric maps of the cosmic 21 cm line signal using LOFAR. Unfortunately, they needed a calibration source to be able to measure this "global signal". The Moon, occulting portions of the field of view, provided a calibration source as they observed that patch of sky.