Sample tetrachoric correlations are computed for pairs of variables at a time because it is numerically intractable to compute them in a multivariate fashion. Because sample tetrachorics are computed in a pairwise fashion we can get non-positive definite sample correlation matrices. Mplus tells you when this happens and claims that the estimates are still valid. Here are the reasons why.
If the assumption of underlying multivariate normality holds exactly, we should in principle have a pos. def. matrix. But the non-positive definiteness should not be of concern for several reasons. First, our estimation techniques do not assume a pos. def. correlation matrix with categorical outcomes. Second, the estimated model has a pos. def. correlation matrix. Third, the sample corr matrix may not be "significantly non-positive definite" in the sense that for a good model the estimated correlation matrix (which gives pos. definiteness) fits the sample correlation matrix well as measured by the model tests of fit.
Some colleagues and I have used MPlus for a CFA of a scale with 11 dichotomous items - which all proceeded very nicely. However, the savedata command gives us a matrix of tetrachorics which is not positive definite. In your post of feb 16 2001 its says that Mplus will give a message when the matrix of tetrachorics are npd. Should we be concerned that we got no such message and yet the output matrix was npd ?