Of course, his ineptness with a gun is something he must be proud of, since he hates them. So I guess it's both things.
In "Swan Song" when Columbo flies to Bakersfield airport to question one of the workers. When the plane is landing, he is holding on to the ceiling of the plane. Also when he gets out of the plane. I found this to be the funniest examples of his fear of flying.
Even though he can stand to look at a murder victim, he has an understandable problem with very detailed forensics photos. You find that out in "Dagger of the Mind."
He hates guns. So much so that he has the murder suspect (Danzinger) fire it into a mattress.
It might be reaching to call this a phobia or an imperfection, but he's easily embarrassed by certain things, like the sunbathing in LOVELY BUT LETHAL or the model in SUITABLE FOR FRAMING.
There's also the first Cathy Goodland and Ken Nichols scene in GREENHOUSE JUNGLE. He doesn't SAY anything, but Cathy picks up on it right away. (Most people would agree with his reaction to it, though I can't help liking Cathy's "I don't care what anyone thinks" attitude.)
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.
Another phobia. He hates hospitals as mentioned in A Stitch in Crime. He gets queasy.