The scene in "Murder, a Self Portrait", when they find Louise dead on the beach, the other two ladies, Vanessa and Julie run up to Max Barsini and comfort him. I could tell that Columbo was easily embarrassed by their reaction and the way they showed the attention to Max.
Forgot one in my original post. Seasickness. He did not do well on the boat in Dead Weight when he went out with the general. Also he embarrassed himself in Troubled Waters when he almost threw up.
This is another very understandable one, so you'd hardly even call it a phobia.
In spite of all the murder victims he's seen, there are some kinds of wound that still get to him. Oddly enough, that includes a wound on a LIVE person, Paul Galesko.