How do you Contrast the considerations that Mill and Kant would advance with respect to what is morally wrong with making a promise that one has no intention of keeping?

What you have here basically is the rather simplistic, but effective, distinction between teleological (Mill) and Deontological ethics. If we quickly sketch out their respective view points, the contrast will become clear.

Mill was the first proponent of Rule Utilitarianism. That is, Ethics was based of a set of rules that were adjudged to promote greatest happiness most of the time. Keeping your promises would be one such rule. Note how Mill's basis for ethics is merely the result - if my some fluke robbery promoted greatest happiness most of the time, robbery would be the correct thing to do. This is what is meant by teleological - ethics is a tool towards an end. So for Mill making a promise with no intention of keeping it is not inherently wrong. If you make a promise to serial killer that you'll hide them, with no intention of keeping it, you're clearly promoting the greater good. This admittedly is a simplistic account of Mill's utilitarianism, ignoring slightly it's rule base, but still holds good.

Kant is different however. For Kant ethical doctrines are logical results derived from reason - this is his notion of the categorical imperative. By the very nature of being Man, we can derive moral propositions from our Reason, which are therefore universal and unchanging, compelling man toward the moral action. The Categorical Imperative (CI) is made more clear through it's comparison to the Hypothetical Imperative (HI). The HI compels action in given circumstances - e.g If you are tired, you should go to bed. The Hypothetical is given in the Word 'If'. But the CI results in propositions such as Do Not Kill. There is no circumstantial qualifier here; the proposition is categorical.

We can put this along side another of Kant's ideas, the Kingdom of Ends, whereby all men must be treated as Ends in themselves, and not as means to an end. These two doctrines combine to present Kant's Deontological ethic - an ethic where the injunction to act well is logical consistency with the Categorical Imperative. So for Kant, you could never make a promise you didn't intend to keep. In the serial killer scenario listed above, Kant could not lie to the serial killer. He would HAVE to tell the truth, this being the very nature of the categorical imperative.

Mill and Kant reach differing conclusions because of the function, and perhaps the ontology, of their ethics. Mill's utilitarianism is very much Human based, and is flexible according to subjective human circumstance. The Kantian approach though is derived from the activity of the transcendent self, and is therefore inflexible whatever the circumstance. The contrast lies mainly in this teleological/deontological distinction.