Some here has posted -- sorry I forget who, but he'll probably jump in soon -- that the exact plot of "Columbo: Uneasy Lies The Crown", right down to details and dialog, was also done on another detective show -- I believe it was "McMillan and Wife".
Unlike Toby's discovery, I assume the casts were completely different.
I recall reading somewhere that Warners Bros used the same pool of writers for all the Westerns and PI series they produced in the late 50's and early 60's (Cheyenne, Sugar Foot, 77 Sunset Strip, etc). Often scripts for one were modified for the other. Is it possible this is the answer for some similarity?