I have consulted with somebody who teach multivariate analysis and she said If you pass Kaiser-Meyer-Olkin Measure of Sampling Adequacy &Bartlett's Test of Sphericity as you said, your analysis will be fine, which is the reason I copied the following notes here. Hope more people join to correct me.
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Kaiser-Meyer-Olkin Measure of Sampling Adequacy - This measure varies between 0 and 1, and values closer to 1 are better. A value of .6 is a suggested minimum.
Bartlett's Test of Sphericity - This tests the null hypothesis that the correlation matrix is an identity matrix. An identity matrix is matrix in which all of the diagonal elements are 1 and all off diagonal elements are 0. You want to reject this null hypothesis.
Taken together, these tests provide a minimum standard which should be passed before a factor analysis (or a principal components analysis) should be conducted.
http://www.ats.ucla.edu/stat/spss/output/factor1.htm
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