Person of Interest : Does Harold have hoplophobia?

I just watched a scene in season 4 episode 15 in which Harold bonks a bad guy over the head with a brass urn and knocks him out. The camera then shows the bad guy's gun lying about 6 inches away from his hand. Harold sees it, hesitates a second, then puts the urn on a shelf and takes Claire hurriedly away.

Watching this I was reminded of Harold's dislike of firearms. I thought, if it were me, I would have at least kicked the pistol across the floor or hidden it so when the bad guy woke up (probably a few moments later) he would not be coming after us shooting.

Why didn't he take the reasonable precaution of making sure the bad guy did not have the gun when he woke up? (When someone is knocked out from a blow to the head, they often wake up within a minute or so.)

He is primarily concerned with preserving lives, making people safe from danger.
Leaving the gun with the bad guy just increased the threat to Claire. And Harold wants to decrease that threat. The logical thing would have been to take the gun, or at least hide it.

It would take an irrational fear of handguns to make him leave that gun with the bad guy.
I wonder if Harold has a mild phobia.

That is probably overinterpreting the thing. He is just the intellectual type, in the episode with the taxi-driver he is described as the librarian, just doesn't go together with arms.
I liked it in the ep. were Carters son gets abducted and Harold is sitting in the car in front of that building and he asks Reese to show him how to use the gun so that he can help, make a distraction or something. Reese just pushes his hand down gently and says you can be the get-away-driver.

I remember that scene too. Yeah, John was probably implying it was a bad idea to learn to shoot on the job. If someone doesn't know how to shoot, they need to be trained in safety basics at a range where they can be watched and corrected.

I recall several scenes where Harold is skittish about guns. When someone picks up weapons as they are going out he sometimes flinches noticeably. They definitely want to show him as being very uncomfortable about guns.

Partly that is to reinforce showing his philosophy that he doesn't want anyone to be hurt (ordinarily). But his flinching indicates an emotional reaction to guns themselves. He doesn't flinch when talking to the three amigos about their use of violence in general, i.e. physically beating people or breaking their necks, etc. He prefers no violence, but he doesn't have the same reaction.

If I watch the series again and make notes on it I can make a list of scenes where he acts scared of guns.

There are a few scenes which are exceptions, but there are plenty of scenes where he displays fear of guns, with flinching or anxiety.

He liked Shaw and Root, so no.

1. He had agoraphobia for like a minute at the beginning of season 2
2. Harper suggested that he has OCD
3. In BSOD he panicked about going on a ferry
4. In SNAFU he spend a week without sleep working on the Machine in the underground and he still had a perfect suit and tie. I know that it fits the convention of the show. James Bond also always has a perfect suit even when his jumping on trains, but it might be a sigh of his OCD.

So yeach he may also have hoplophobia. I personally think that psychology students could use this show to practice. All the characters, apart from Carter, have some form of psychological problems. Bear started normal but he's getting increasingly spoiled and oversensitive from living with four dysfunctional adults who pour all their love and unfulfilled parental instinct into him.

Harold did once hold a shotgun because he was about to break Reese out of prison(?)

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yeah, it isn't consistent throughout the show. Since it is television and not reality, the characters can change at the whim of the writers. There are a few times when he holds a gun.
But in the majority of scenes where Harold is around guns he expresses either dislike, or he flinches or acts scared of them.

It could be argued that this only represents his opposition to violence and not an irrational fear of weapons.

It is the flinching he sometimes exhibits which makes me think of hoplophobia.