“Clara is just a plot device in a skirt!”
This is a criticism which was thrown a lot at Clara in Series 7. One which holds water at a glance. But especially given what we learn about her character in Series 8, I believe there is plenty of room for interpretation in both hers and The Doctor’s actions and attitudes which, even if not intentional, may help someone enjoy her arc on a deeper level.
First I want to address the criticism of Moffat that his companions, and Clara in particular, aren’t normal enough; to do that I think we need to look at The Doctor. One of Eleven’s defining character traits (or tawdry quirks) has been picking out details which aren’t what they seem – he is exceptionally analytical and a strategic thinker. But he has been known to miss the obvious by wanting to make it clever. Emotions also get the better of him, and following The Angels Take Manhattan, he is both grieving and has lost the people who usually call him out for making those mistakes.
Even under normal circumstances it would be very much in-character for Eleven to be attracted to someone who is a ‘puzzle’, just as it was in-character for Nine and Ten to latch on to ‘normal’ humans in an attempt to rebuild a sense of belonging following the Time War. But here, Eleven’s grief gets the better of him and he distracts himself via his fascination with the mystery of the impossible girl – overcomplicating it and frequently forgets the woman behind it.
Now there is a lot of wiggle room in this post, but this I definitely think was intentional because The Doctor is called out for it repeatedly, by Emma Grayling, Clara herself, and Madame Vastra. But even as late as Nightmare in Silver it is clear he is preoccupied by the version of the impossible girl he has constructed. And because he does, so do we.