There have been several important studies of interviewer variance in face-to-face surveys. O'Muircheartaigh and Campanelli (1998) report on a study that used an interpenetrated design to evaluate the impact of interviewers on variance estimates.
There are also studies that show interviewers vary in their ability to establish contact (Campanelli et al., Can you hear me knocking? 1999) and elicit response (Durrant, Groves, Staetsky, Steele, 2010).
Although O'Muricheartaigh and Campanelli account for the clustering of the sample design, they don't account for differences in response (due to contact or refusal). It may be that variation in response rates or the composition of response may explain some (certainly not all) of the interviewer variation.
If that is the case, then attempting to control interviewer recruitment protocols (like call timing) might help reduce interviewer variance.