The Mishna Berura (252:17) cites the Hayeh Adam (Rav Abraham Danzig of Vilna, 1748-1820) who rules that one may not allow a technician to remain in his house on Shabbat to complete repairs. Even though the technician is working on the basis of "Kablanut," a fixed fee per task, it is prohibited, because of "Marit Ayin." Outside observers may misconstrue the circumstances of the employment.
There is one exception to this principle. In cases where there is an issue of "Kavod Habriyot" (Human Dignity), e.g. a plumbing emergency, one may allow the technician to complete the repair. The Halachic weight of Kavod Habriyot overrides the concern of "Marit Ayin," which is a Rabbinic enactment.
SUMMARY
One may allow a technician to complete repairs in his home on Shabbat under circumstances compromising "Kavod Habriyot."
