A) If you could prove it, it would invalidate the marriage contract, since marriage is necessarily exclusive, indissoluble, and for life. That's why most priests won't participate in a wedding unless the couple attends some kind of marriage preparation classes, where they learn that "marriage is for life, to one person" and other important things.

B) It would mean he's starting his marriage out on the wrong foot, in mortal sin, and I see a bad marriage coming -- but I don't see how any mortal sin, even of the flesh, would invalidate a marriage. It would have to be a sin which *affects the nature of marriage itself*, such as threatening the priest with death unless he marries them, lying about who you are, hiding the fact you had yourself sterilized, etc.

Again, a down-to-earth, vague "OOOOOh, That's just WROOOOONG, sista!" is not the same thing as something that invalidates entering into a valid marriage contract. We have to reason with our HEADS, not with our hearts.

This is correct.

Two examples from real life:-
The man has a mistress from several years before meeting his wife to be.  He already has a child with her and she is six months pregnant with his second child at the time of his wedding.  His wife and her family know nothing of it.  They remain married for six years, have two children and are expecting a third when he blows his cover by an unwise financial move.  The mistress knew about it the entire time and was “okay” with it! She was baptized Catholic and he was baptized Lutheran who agreed to raising the kids Catholic, etc.  They got a dispensation. He even went to Mass when he wasn’t “working.” 
Isn’t deliberate deception of a serious nature a legitimate reason for annulment?

A dating couple, both Catholic, discuss marriage. He wants to get engaged, but she’s not sure.  The reason is because she’s been seeing someone else, unbeknownst to him.  They let things go on too long, and she sleeps with the side-lover, becoming pregnant.  He’s not neither Catholic nor a marriage prospect.  When he finds out, he offers an illegal abortion or farewell. She takes the farewell, and then seduces the other man to sin. After thus sinning a number of times, she tells she’s pregnant.  Wanting to do the honorable thing and make it right, they get engaged, go to confession, and have a small Catholic marriage ceremony. The baby girl looks very much like her mother, and as she grows, several distant relatives who knew of her former boyfriend begin talking.  The child begins to resemble the ex-boyfriend and not her father at all.  The marriage isn’t going well.  She says she doesn’t want any more children, and she eventually requests a divorce.  He is most upset, having been trying to be a good Catholic father and husband.  But finally she leaves him for another man and is soon carrying his baby.  They get a civil divorce leaving the girl in his custody.  He gets drafted and custody goes to the mother when he’s deployed to Vietnam. He ends up in country for seven years.  When he returns, his daughter doesn’t know him, doesn’t want to know him.  He spends the next five years being reviled by the general public as happened to most Vietnam vets.  He’s got PTSD, turns to drinking and drugs, but finally, his mother’s prayers are answered.  He gets help, moves in with his brother’s family and his mother, goes back to Church, finds work in construction. He meets a widow with four sons, one still in high school.  She’s Catholic, too.  He knows his ex is still alive, so he says he can’t marry.  She convinces him to request an annulment.  Not surprisingly, he’s granted one by the now VII church.  Still, he doesn’t feel quite right about it.  Again, it’s Mom who has the idea.  She remembers the talk from years before. It takes two years to convince his daughter to consent to a DNA test.  Sure enough, there is no way the two are related. Although not her fault, the daughter is furious and sues her “father” and “grandmother” for defamation, deception, emotional distress, etc.  They lost all but one aspect of the case.  They had a full Church wedding, etc.  About 10 years ago they began attending an Indult Mass, and after it’s relocation at a distance, looked into Mass at an SSPV chapel. When shown the annulment certificate, along with the DNA test, and told the entire story, they’re still barred from receiving the Sacraments. One priest said there’d have to be a statement from the ex wife admitting to deceiving him into marriage.  But that didn’t happen as the ex was by then in a nursing home suffering from severe Alzheimer’s disease.  She has since passed away.
Now that his ex has died, couldn’t they now go to an SSPV chapel?  Whether or not they’d recognize the annulment shouldn’t matter.  You cannot be married to a dead person, right?

Uh, negative.  As a whiny, lazy punk who asks for sources he could get himself, that you would offer such groundless, trash input on such a serious matter is most disconcerting, although not remotely surprising. 

Any serious lie before marriage invalidates the traditional Catholic vow. 

B) if he was in the habit of having sex with others while courting the new wife and she didn't know about it, he didn't tell anyone, and he continued adultery in the marriage, that would invalidate...

Any serious lie before marriage invalidates the traditional Catholic vow.

I think any lack of full mental capacity at the time of the initiation of the marriage , like drug abuse, alcoholism schitzophrenia etc is a possible cause for a true annulment.

Some actually say immaturity is a reason ,but that would have to be really severe, as far as I can fathom.

Any coercion, like a shot-gun wedding, where someone does not have full intent of the will can be a reason.

The intention to not want children, or to limit children which was not revealed to the intended spouse before the marriage is a cause also.

Along with sɛҳuąƖ relations/affairs with others at the time of the marriage unknown to the potential spouse and or bigamy obviously is a reason.