"No Ties, No Jeans" doesn't bother me in the least. It's communicating in a way the intended audience* understands. I doubt many tweens/teens know what "business casual" or "yacht club" attire means.
*I'm assuming the guests are not adults.
As I posted above, the guests ARE adults -- some kids, but it's not a kids' party, it's an adult dinner dance, to which there are kids invited. (I know this string has gotten long and you're not required to read all the posts before posting!) Does that change your feeling?
The fact that so many people are saying that they like this wording specifically "because it gives guidance to kids," because kids have different standards of dress and can't really be expected to know the social language of "casual," "business casual," etc., underscores for me what's not so good about it for adults. It implies that their social skills are those of children who can't be expected how to interpret a dress code without specific guidance.
Now that I think about it, I've seen something like this in practice. If there are a lot of children invited to an adult-type event, sometimes people send them a separate invitation (like, if the children are invited for different hours than the adults -- e.g., pizza and games for the kids 6:30 - 8:00; dessert and dancing for everyone at 8:00 -- I guess it's A and B, but I for one am definitely NOT offended by not being included in the children's "before party"!). Anyway, when they do that, people often include things like "please no jeans/shorts" or "no gifts" or other stuff that they don't put on the adult invitation.
As to the suitability of denim generally for a grown-up event designated "casual," I think it may depend upon the community (both geographic and social) -- of course assuming it's not a no-denim venue. If nice denim is not
considered acceptable in the relevant community, then there is no need to include "no jeans" on the invitation -- most of the guests know already (as they would here), and if there are a few who don't, then too bad -- you don't insult/micromanage all the others trying to make sure that not a single guest wears jeans, the same as you don't put "no tardiness." If denim is
considered appropriate in that community, then I honestly don't think that the hosts should be trying to forbid it at their otherwise casual party, just because they personally don't like that "casual" includes jeans in their community -- just like they shouldn't say "no short dresses" if they designate the party "black tie" and live in a community where women wear long or short dresses to black tie events, but happen to prefer that all the women wear long gowns. If it means that much to them not to have anyone in jeans, then, if they live in such a community, they should call it "dressy" or "business casual" or something other than "casual."
As for the other end of the question, "no ties," I think that Peaches's point about stating things in the negative is spot on here. "Ties not required" is much better. Even if most people would figure that "no ties" means "ties not required," they wouldn't be 100% sure, and you can bet that if you wear a tie, there'd be at least one idiot telling you, "Hey, the invitation said no ties!" (The conversation that would follow would resemble this string!)