I have a large dataset containing several objects. Each object has many attributes which is arranged in a time series. Is there a suggested method to find the top n "most interesting" attributes? The data contains many missing values so by "most interesting" I mean an attribute that has most of its values filled in as well as one that has some diversity in those values. For example, I'm not interested in the attributes that have all values filled in but have only 2 distinct values. Does this sound like an information theory problem? I'm not sure what I'm looking for here so any help would be appreciated. Thanks.

Edit/Clarification:   

Thanks for the input so far.   

By "missing values" I mean that right now they take on the value of "NaN"   

"I'm not interested in the attributes that have all values filled in but have only 2 distinct values" - by this I mean, for example, if one attribute can take on any value between 0 *and* 255 but all the values are either 0 *or* 255 then I wish to ignore this attribute.

All the of the values were manually entered so I wouldn't consider it supervised/unsupervised.