"dis" and "un" prefixes for the word interest

Solution 1:

I thought I'd better offer an answer rather than a comment here, after doing a little research.

Traditionally, there was / is a famous distinction between uninterested (heading towards bored) and disinterested (impartial), but the distinction is apparently (and sadly) becoming blurred. Though many people would want to maintain the useful distinction (I'm one of these), English is ultimately a communication tool, and we must bear in mind the ways a substantial proportion of speakers use words. These change over time, and the process seems largely unavoidable, even in cases where people more interested in the language per se than the majority of speakers are consider the changes for the worse.

At http://grammar.about.com/od/alightersideofwriting/a/disuninterest.htm is a fine series of comments about the uninterested / disinterested debate, including discussions about how far the blurring has gone / 'is acceptable'. The AHDEL has a valuable usage note:

In traditional usage, disinterested can only mean 'having no stake in an outcome,' as in Since the judge stands to profit from the sale of the company, she cannot be considered a disinterested party in the dispute. But despite critical disapproval, disinterested has come to be widely used by many educated writers to mean 'uninterested' or 'having lost interest,' as in Since she discovered skiing, she is disinterested in her schoolwork. Oddly enough, 'not interested' is the oldest sense of the word, going back to the 17th century. This sense became outmoded in the 18th century but underwent a revival in the first quarter of the early 20th. Despite its resuscitation, this usage is widely considered an error. In a 1988 survey, 89 percent of the Usage Panel rejected the sentence His unwillingness to give five minutes of his time proves that he is disinterested in finding a solution to the problem. This is not a significantly different proportion from the 93 percent who disapproved of the same usage in 1980."

(The American Heritage Dictionary of the English Language, 4th ed., 2000)

Solution 2:

OED has

uninterested

†1. Unbiassed [sic], impartial. Obs.
†2. Free from motives of personal interest; disinterested. Obs.
3. Unconcerned, indifferent. In this sense disinterested is increasingly common in informal use, though widely regarded as incorrect: see disinterested adj. 1.

disinterested

1. Without interest or concern; not interested, unconcerned. (Often regarded as a loose use.)
2. Not influenced by interest; impartial, unbiased, unprejudiced; now always, Unbiased by personal interest; free from self-seeking. (Of persons, or their dispositions, actions, etc.)

So uninterested is indifferent (that is, the subject is of no interest or note). Disinterested may also mean that, but that would be to use the word loosely; less loosely it means unbiased.

From uninterested comes uninteresting — of no concern, not noteworthy, trivial.

Thus someone may be disinterested in a subject without it being uninteresting. It is not altogether correct to say "I am disinterested in that topic" means the same as "That topic is uninteresting."

The usage discussion in MW to which you refer makes much the same point. Since we have two words which have evolved to have distinct and useful meanings it is a shame to confuse them in loose usage.