I favour D'Arcy Thompson's view. If you are precisely wrong, it will be easy for evidence to refute you and make you less wrong. But if you are already vaguely right, how will you attain to being precisely right? How will you discover that you are actually vaguely wrong, if your wiggle room lets you explain away contrary evidence? As Francis Bacon wrote, "Truth arises more readily from error than from confusion."

Being vaguely right is only better when you need to decide an action now and have no opportunity to improve your knowledge. But being precisely right is better still. "Weak Bayesian evidence" is worth as much as a penny lying in the road: if you need to pick up a penny, you need a lot more than a penny.

But in fact, that is not the sort of vague rightness that the quote you linked to is about. Here is its context:

The terms of ordinary language fall into the same classes as those of science: they stand for things, classes of things, parts, or qualities, or activities of things; but they are far less precise in their signification. As long as popular thought is vague its language must be vague; nor is it desirable too strictly to correct the language whilst the thought is incorrigible. Much of the effect of poetry and eloquence depends upon the elasticity and indirect suggestiveness of common terms. Even in reasoning upon some subjects, it is a mistake to aim at an unattainable precision. It is better to be vaguely right than exactly wrong. In the criticism of manners, of fine art, or of literature, in politics, religion and moral philosophy, what we are anxious to say is often far from clear to ourselves; and it is better to indicate our meaning approximately, or as we feel about it, than to convey a false meaning, or to lose the warmth and colour that are the life of such reflections. It is hard to decide whether more harm has been done by sophists who take a base advantage of the vagueness of common terms, or by honest paralogists (if I may use the word) who begin by deceiving themselves with a plausible definiteness of expression, and go on to propagate their delusions amongst followers eager for systematic insight but ignorant of the limits of its possibility.

Carveth Read, Logic: Deductive and Inductive, p.351.

Popular thought, poetry, eloquence, manners, fine art, literature, politics, religion and moral philosophy. Is our "vague rightness" in such matters anything more than an illusion, a subjective sense of "meaningfulness" when we utter our words that has as much backing as a sub-prime mortgage?

ETA: That last sentence of the extended quote is rather good, and deserves to be quoted on its own. ETA again: except the final phrase: such people are up against the limits, not of its possibility, but of their own capacities.