Is there any way to know if the labels of certain observations in the training set were misplaced to begin with?
Not from the values in the data set; you may be able to trace back through the data source to identify potential mislabelling, but normally you can't know that values were mislabelled just from looking at them.
There are some exceptions - if your data are on different types of operations, a Caesarian section on a male, or a person 183 inches tall may be a pretty clear indication of 'mislabelled' data, but outside of that kind of logical identification, strange values cannot normally be known to be mislabelled.
Even if I do find some observations that are likely "outliers", based on model's studentized residuals OR Mahalanobis Distance etc, how do I know that it is not due to model bias? Since the model may not capture every detail.
You usually don't -- outliers are outliers with respect to some model for the data. A different model may regard values as perfectly reasonable; you might come to regard some observations as unusual under a variety of reasonable models, or perhaps even conclude that no reasonable understanding of the data would make those points in accord with the rest but - especially with categorical responses - such situations aren't the most common.
How do I go about choosing another class label for these records?
If the data are implausible, you might treat the implausible value as missing and use missing data methods. If the label were missing, how would you fill it in?
One approach is to use model-based imputation: If you were making a prediction at that set of predictor-values, what would your predicted value be?
You may want to consider that there may be several quite plausible categories; it's worth considering multiple imputation methods.
There are many other approaches to imputing missing values, and numerous books with sections on the topic (there are also whole books, such as the one by Little and Rubin).
For example, there's a short discussion of a variety of approaches in Gelman and Hill's "Data Analysis Using Regression and Multilevel/Hierarchical Models". See here. While that's not explicitly about your particular model, many of the approaches discussed do carry across.
