Hey folks, copy & paste this if you're interested:

http://pqasb.pqarchiver.com/USAToday/access/55880862.html?dids=55880862:55880862&FMT=ABS&FMTS=ABS:FT&type=current&date=Nov+09%2C+1988&author=Matt+Roush&pub=USA+TODAY+%28pre-1997+Fulltext%29&desc=Falk+and+%60Columbo%27+are+back+on+the+case&pqatl=google

An archive article from USA Today about the return of Columbo in the 1988-89 season, including when they started filming. It seems "Murder, Smoke and Shadows" was made first.

I found this via Google's free newspaper archive. More Columbo gems to be found here:

http://news.google.com/newspapers

I also discovered that "Murder With Too Many Notes" began filming Tuesday 17th November 1998.