Dear Aydin
Good questions and having various perspective. The depth means the accurateness of data (what I consider). The only limitation is that how to measure the accurate value for any variable. Since it is not possible to ascertain therefore we are using the term precise (average measurement). So depth of measurement should be a theoretical concept.
The word "depth" is not used in research books, instead the used terms are: Validity, reliability, sensitivity, accuracy and all included under the term: psychometrics of the measurement.
Depends on research paradigm; agree with the two answers above, in quantitative terms; however, in qualitative research, the 'depth' of 'measurement' is how far into respondents' 'life-worlds' one intends to go; from this point-of-view, I think, there is no definite limitation.
I think it has something to do with least count for a parameter for a body with respect to its over all size. For example if we are measuring a crop field, measurement upto a least count of mm will be considered as extremely good depth of measurement. So it would be relative term depending upon the size, parameter and least count in a given situation.
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