Why was the incestuous (not sure about spelling) relationship between Mary and Vincent not a big deal in part III? Michael disapproved of it because it was "dangerous," and Vincent had his doubts for the same reason. I get the feeling that it didn't even bother Kay as she tells Michael, "your daughter is in love." But, the bigger issue is that they are FIRST COUSINS! Why was that just "glossed over" in the film? Am I missing something?

Welcome, Just Watching! Thoughtful question!
Yes, it was technically "incest," according to law: Vincent and Mary were blood relation first cousins. The only explanation I can think of was that perhaps Puzo was thinking of Paul Castellano:
Castellano married his childhood sweetheart, Nina Manno, who was Carlo Gambino's sister in law. What's more, Gambino was married to Castellano's sister. And Gambino had married his own first cousin. These complicated ties cemented Castellano's rise in the Gambino Family, much as European royalty intermarried to cement alliances throughout history. In GFIII, it underscores Vincent's ambition to rise in the Corleone Family, and to succeed Michael.
Vincent was a very manipulative fellow, a side of his personality that doesn't get much attention.

On Vincent, I always felt he didn't love Mary sincerely. For that matter, how many of you agree with me that Vincent had no true love, or ambition, apart from control of the Corleone family?

I believe he would have betrayed Michael if that fulfilld his ambition.

Well, first-cousin marriages are legal in a number of U.S. states. I think the reason it was done that way in the script was to make it a very morally ambiguous relationship - not quite illegal but certainly very questionable.

Also I think the idea was to create the idea that Michael ultimately might have Vincent hit, if it came to that.

I never liked the whole cousin-romance thing anyway. I would have rather seen Vincent pursue his romance with Grace Hamilton (Bridget Fonda) -- a reporter who would be inclined to try to dig into the family's inner business -- and thus pose a threat to the family's security in that way.

Ultimately if Grace were to marry Vincent, she would know the extent of what he was into - and she would either have to expose him, or cover for him. (Become one of the 'newspaper people on the payroll' Tom Hagen refers to in GF I.)

This would be a topic for possible GF IV - as Michael returned to Kay after seeing Apollonia killed, Vincent would return to Grace after seeing Mary murdered.

Well I think Vincent loved Mary, it's just that he loved the thought of being the boss of the Corleone family even more.

But I don't beleive that Vincent would've ever betrayed Michael. Cause I've always felt that Vincent knew that Michael had Fredo killed, due to Fredo betraying him. And Vincent didn't want to end up like Fredo. Course that's my 2 cents worth.

AS for the whole incest thing between Vincent/Mary that never bothered me in the least. Course I'm not sure what that says about me.

I don't think we as the audience are given enough information or not to determine Vincents true feelings for Mary. We know he's a bit of a playboy and would probably fake any feelings to get into bed. Mary on the other hand really did love him.

It's lately occurred to me that this was probably more of Puzo's idea than FFC's. In Puzo's The Family, he writes about a Renaissance powerful Family, a story he wanted to tell for a long time that included an incestuous relationship to solidify the power and loyalty of the Family. Maybe before he got the chance to write the Family he wanted to use the same elements (also seen with the King and three sons).

I guess the whole Vincent/Mary relationship was one of the main reasons I didn't care for GF3. I know a lot of you will probably disagree with me but it seems like they took the easy way out by creating the Vincent character in the first place. Since all of us who have read the novel know Lucy (Vincent's mother) never had a child by Sonny.
With Vincent and Mary you couldn't detect any kind of chemistry, say like there was between Michael and Appolonia, you know,"the thunderbolt" kind of passion.

First cousin relationships are not incestuous- improper maybe, even illegal in some areas, but technically not incestuous. i really didn't mind the relationship, especially considering that it was made clear that Mary and Vincent hadn't see each other in years.

Someone mentioned Grace up there and it reminded me- What the hell was she doing in this movie? Just another big name and pretty face to take up screen time to draw the viewers attention away from the plot weaker than hot butter?

I myself wondered the same thing-she was there and then disappeared...

That's very true, but I think that was more due to Sofia Coppola's lack of acting ability...perhaps a better actress could have made the relationship more convincing.