So looking at your standard domestic dog from an angle that takes in the face but does not take in genitalia, can people tell the difference between male and female with any accuracy? If so, how?
Taken in male/female pairs of the same breed to compare against each other, probably most people could make a decent guess. Like the vast majority of mammals, dogs are sexually dimorphic with consistently larger, bigger-boned males. Male features are larger and heavier - this tends to be most pronounced in the head and shoulders.
However without a direct comparison it becomes a bit tougher - someone experienced with a particular breed can probably still do a fair job, but a random non-dog-owning person with a random individual mongrel is going to have a tougher time of it. This is particularly the case if you have a young dog - the farther from sexual maturity, the less dimorphic they’re going to be.
and here
Two Golden Retriever (Canis familiaris) female and male adults sitting side by side
Given two purebred dogs of the same breed, one male, one female, the male is usually larger. Larger in total size and larger features as well. Larger paws, broader jaw, bigger chest, and many other features. For brother and sister dogs it can be very obvious. However, your standard domestic dog isn’t registered with the kennel club and looking at just one dog so you can’t compare a male and female it will be difficult to determine accurately. At that point you’d look at behavioral characteristics as well as physical features, but you still couldn’t be sure without a closer examination of certain parts.
Sure, you can. Of course it involves a mouth swab and the involvement of a DNA lab…
It’s amazing what you can train a lab to do these days. 
It’s easier for some breeds than others. With collies, for instance, males have a thick mane that the females lack (which made it especially silly that Lassie was played by a male dog).
For features within one breed, for instance - in collies the male retains a thicker coat year around, whereas the females shed their coats massively twice a year in conjunction with coming into season. This is one reason they used male collies to portray Lassie. Females would not have looked as photogenic for a few months a year. And apparently, spayed females develop thick coats, but they don’t have the right appearance.
ETA:
Chronos’ post crossed mine (yeah, I know … I let it hang about for several minutes before clicking “post”).
Well, this one is easy to tell, the one on the right is the male. 
Seriously, though, often I can tell by how they sit, but you can be fooled. My brother had a male dog that would “sit like a girl”, and he get that comment a lot. Females tend to splay their legs more when the sit or lie down.
Just check for an adam’s apple.
Head shape and overall conformation provide clues, but to be sure I’ve got to sniff their butt.
Sometimes you can use external cues. But even that may not be enough. One time I was introducing one of my dogs to someone: my dog was wearing a pink shirt that said “Queen of the Dog Park” in glitter, and I said, “Her name is Simone.”
The person smiled and asked, “Is he a boy or girl?”
I wanted to say, “I can’t possibly give you any more clues.”
The female is the one wearing lipstick.
(may be confused with a soccer mom)
Or a pig.
Check the name on the tag. “Princess” is probably female, “Prince” is, well, you figure it out.
“Shadow” won’t help, though.
I have 7 Jacks and my vet remarked that they are the first dogs he can easily tell which is male and female from their faces. All the girls faces are thinner.
NM… beaten to the punch.
I can for the breeds I know well, German Shepherds, Huskies, Poodles, Golden Retrievers. . . Obviously I won’t get it 100% of the time, but there are differences in how the face, size, bone structure and especially musculature develop in the presence of different hormones. If they were fixed at an early age the differences are much less. In the world of pets vs show dogs, I’d bet I 'd have a lot more trouble.
In some cases I can even tell a bitch that has whelped from one who hasn’t. Again, not 100% but I’ve got a darn good track record.
About half the time, yes.
Unless the dog is cis- or transgender, and has opted for a chondrolaryngoplasty. Plus, considering the gender-boggling sexual and dominance humping that goes on in canine society, your assumptions will be all the more suspect. Coincidentally, a related thread here is moving long nicely, About transgenders (transexuals?) and sexual orientation.
Human women do have the same “apple” (luckily), the cricoid cartilage, and you can see it. It’s just positioned differently and looks different (I like this page’s type of anatomical discussion/observation a lot).
Dogs have them too (luckily). Diagrams and full details here; little flat-faced dogs are severely in trouble if they are damaged. In fact, research in the canine anatomy was and is crucial to every human intubation and reflux procedure done today.
IANOvet, just bored and Googling.
Of course I have not answered the question: do male and female dogs have different cricoid cartilage anatomy.