Re: the 1975 Sears Catalogue Men’s Briefs photo, I remember that one pretty well. My uncle, whose sensibilities tended towards the lowbrow, had a copy of the catalog and a 45 single of a novelty song someone had recorded about it (Sample lyric: “How I wish/I was the man/On Page 32” or whatever).
IIRC, the photo was in color, printed pretty well, and there was an obvious blemish of some sort that wasn’t the guy’s penis.
What can I say? Mom’s brothers were easily amused.
I found a copy of this catalog when I went through my mother’s stuff after she passed. At first I thought “Hmm, I wonder why mom kept this 30 year old wish book.”, but then I remembered the Straight Dope article and thought “Naa, it couldn’t be.” Turns out that it not only could be but is was. There was the “schlong” peeking out of the boxers (it was originally in black and white as Cecil’s pictures represent).
Unfortunately, even with the actual catalog in hand, I cannot 100% confirm that it is a penis. Having been in the print business for 15 years I can tell you a couple of things that it is not. It is not a “hickey”. Hickeys are usually caused by dust or debris on the print plate. Even a microscopic spec of dust has the potential to displace enough ink to cause a visable defect. However, for the defect to be that big the particle would need to have been large enough to have it’s own print pattern, leaving the defect with a spot in the middle of it looking more like a nipple than a hickey. It’s also not a water spot. Water tends to pool and form a more uniformly round blemish. I suppose it’s possible for a water spot to be misshapen enought to cause the blemish but I doubt it.
IMPO it is an unidentified object in the original photo. Could be a penis, could be some sort of fabric or string, could just be a nasty case of ringworm in an awkward place. In any case there was something there in the original picture that could have and should have been airbrushed out and was either missed or left intentionally for publicity. Heck, as far as I know it could have been airbrushed in for publicity or as a prank.
Printing and boxmaking can be an interesting business. Two examples that come to mind are a TV box we made many years ago that featured a man laying in bed on his back with a sizable (but relatively unnoticable to the untrained eye) tent in the sheet and a display base that had a locking tab designed to look more like a penis than a standard locking tab (gave new insight to “Insert tab A into slot B”). Us boxmakers are a strange breed, I figure all pressmen are in one way or another. Probably due to the ammonia fumes coming off the ink (I miss those sometimes).
Doesn’t look like a cock to me. Just looks like a shadow or printing defect.
Snopes has a link to it.
I was a snickering adolescent in 1975, and remember the ad, the hoopla and the resulting novelty song well. My memory is that it looked like a penis-like thing, but was too translucent to be the real thing. I remember my mother letting us scrutinize it all we wanted; my conclusion then was that is it was really bad, she wouldn’t let us look.
It seems like the name of the song was “The Man on Page 302” (or whatever the page number was).
Looking back, it appears the public was starved for the naughty in 1975. 
Nitpick: the model is wearing boxers, not briefs.
I’ve worked at the Sears catalog’s printer, RR Donnelley, for some time, and have heard the skinny from people who used to work on the catalog:
Protuberances from happy male models are a common problem in catalog photography, as are erect nipples on female models. In the print business, they were called “potatoes” and “headlamps,” and it was standard procedure to have them airbrushed out. This photo just happened to slip by the proofreading process.
Now, there are also stories about touch-up artists who were fired after it was discovered they had worked the folds in a set of draperies into various 4-letter words…