I built the antenna found here: uhfhdtvantenna.blogspot.com/ except I used 14 AWG copper wire for the whole thing instead of wire hangers and without the reflecting part. I connected a 300 to 75 ohm balun to it and then to 25' of RG6.

I noticed that the antenna was very directionally sensitive. While I was moving it, I accidentally touched the screw portion of the F connector to one of the antenna elements and the signal on my DTV box went to about 60-70%. Once I moved the RG6 so that the connector didn't touch, the signal dropped to 0.

I unhooked the RG6 from the converter box side. I took my digital multimeter and found there there is no connectivity between any antenna element and either the center conductor on the other end of the RG6 or the outer sleeve.

I put the RG6 back to the converter box and unhooked the RG6 from the antenna. I connected the antenna to the RG6 using two jumper leads and I had better signal compared to using the 300 to 75 ohm converter.

Is this balun defective?

The balun may be defective but continuity doesn't mean anything; most of them are transformer-coupled and won't show any continuity on a meter.

A balun is two coils interwoven. They do not touch so you will not see continuity from the antenna side to the coax side. If you check for continuity from terminal to terminal on each side, you should show a short but not across the balun. Balun is actually two words run together, balanced/unbalanced because you are taking a balanced source, the antenna to a unbalanced load, the coax and through an electromagnetic field, connecting these different terminations to allow the RF to flow from the balanced antenna to the unbalanced TV.

I am not familiar with balanced/unbalanced circuits, but I am familiar with the transformer/inductive coupling concept. So I would need an AC signal to get a signal to pass though the balun and I am assuming that my DMM uses DC signal when measuring resistance and the continuity function so nothing would pass.

On the 300 ohm side of the balun, I have 0.2 ohms which I would consider a short.

On the 75 ohm side, I attached a 6 ft piece of RG6 and found no continuity between the center and side; there is infinite resistance. I know that the RG6 works since I took it from a functional cable modem setup.

This should be sufficient to conclude the balun defective, correct?

A balun is two coils interwoven. They do not touch so you will not see continuity from the antenna side to the coax side. If you check for continuity from terminal to terminal on each side, you should show a short but not across the balun...

That's what I thought, until I found several that did have continuity from input to output. One of the drawings in my twenty-something year old ARL book shows a connection between coils in one of its balun drawings.

As a rule, the tiny, "indoor" penny Tootsie roll sized baluns short between one input and one output, whereas the physically larger ones, commonly called outdoor baluns, generally isolate but not always.

The Radio Shack balun with a push-on "F" connecvtor and screw terminals for 300 ohms, which was designed for adapring an FM "T" antenna, definitely has isolated coils, but unfortunately, its frequency flatness at UHF frequencies is irregular.

I got a replacement converter and it works better.

While adjusting the antenna one of the leads came off from the screw in the wood and the some channels worked better this way. Why?

I also found that holding the RG6 or putting my hand near (not touching) the array could sometimes improve reception. Am I, in effect, becoming part of the antenna when I do this?

I also found that holding the RG6 or putting my hand near (not touching) the array could sometimes improve reception. Am I, in effect, becoming part of the antenna when I do this?

Yes. Most likely you're changing the impedance of the antenna. Chances are your antenna is not a good match for 300 ohms at UHF -- check the very long thread on building your own UHF antenna here for designs which are better than the one at blogspot.