What's the difference between "obscene" and "scatological"?

Solution 1:

"Scatological" is only ever used to refer to feces.
Although @Malvolio makes a distinction that "obscene" specifically refers to sexual content, that's not necessarily the case:

–adjective 1. offensive to morality or decency; indecent; depraved: obscene language. 2. causing uncontrolled sexual desire. 3. abominable; disgusting; repulsive.

We (Americans, anyway) often use "obscene" to simply mean "outrageous":

He made an obscene amount of money selling sub-prime mortgages.

Despite Freud's conflation of money and feces, I can't imagine ever saying "a scatological amount of money."

Solution 2:

Obscenity has a specific legal meaning in the US:

the average person, applying contemporary community standards finds that the work, taken as a whole, appeals to the prurient interest; the work depicts or describes, in a patently offensive way, sexual conduct specifically defined by applicable state law, and the work, taken as a whole, lacks serious literary, artistic, political or scientific value

Obviously, people aren't constrained by the legal definition of words any more than by the dictionary definition, but personally, I try to hew close to the legal definition whenever it might seem I am offering an opinion on a legal matter.

So traffic might be "murder" and my boss's salary might be obscene, but a death in a traffic accident is "manslaughter" at worst and "shit happens" is merely vulgar.