If still interests you here goes one solution.
Train your network with a training set with all the inputs that you will further on analyze. After learning, you give the new test data to classify with only the inputs that you have. The network give you back which was the best matching unit (for the features you have), and with this you can access to which of the features you do not have/outliers the BMU corresponds to.
This of course leads to a different learning and prediction implementation. The learning you implement straightforward as suggested in many tutorials. The prediction you need to make the SOM ignore NaN and calculate the BMU based on only the other values. After that, with the BMU you can get the corresponding features and use that to predict missing values or outliers.