The matfile documentation states "The MAT-file object does not support indexing into... Cells of cell arrays..." This means you can use parenthesis indexing to return the cells themselves, but not curly-brace indexing to access the contents of the cells:
"Is there a way to load part of a cell array that has been saved to a .mat file?"
Of course, you can use parentheses (which will return a cell array, from which you can trivially access its contents):
>> C = {'hello','world',NaN};
>> save('test.mat','C','-v7.3');
>> clear
>> M = matfile('test.mat');
>> D = M.C(1,2)
D =
'world'
>> S = D{1}
S =
world
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