Two hundred patients with abnormal symptoms, but no signs of any concrete medical diagnosis, were divided randomly into two groups. The patients in one group were told "I cannot be certain what is the matter with you", and two weeks later only 39% were better"; the other group were given a firm diagnosis, with no messing about, and confidently told they would be better within a few weeks. 64% of that group got better in two weeks." (Bad Science, p. 75, citing Thomas 1987)
I can imagine a lot of factors that could affect the effectiveness of the doctor's words here - mainly anthropological, but some of them would certainly fall within the domain of linguistics. For example, the intonation pattern will affect the patient's perception of the doctor's confidence; does that affect the efficacy? Likewise, the accent and the choice of vocabulary could both affect comprehension and perceived competence, and hence presumably the efficacy. Not really my field, but it could be a line of research with unusually clear-cut potential benefits. The obvious problem with this example is that it involves doctors lying to patients, but if the effect could be reproduced without that it would certainly be worth doing.
Thomas KB. General practice consultations: is there any point in being positive? BMJ (Clin Res ed) (9 May 1987); 294 (6581): 1200-2.