9. River Learning The Doctor's Name
Forget the sonic screwdriver and Tardis book, what really put River Song on the map as an important character was her knowing the Doctors real name. The shows biggest mystery since it's inception, having a character know it was a bigger deal than the Daleks returning, again. Fans jumped at the theory that River knew this because she was his future wife, having learnt it at their wedding. This was initially confirmed in The Wedding Of River Song when the Doctor said as such to the audience, until five minutes later it was revealed hed said something completely different. The problem here is obvious; if the Doctor said look into my eye (revealing he was actually the teselecta) instead of his name, when did River have an opportunity to learn it? The implication for the Library two-parter was that there was only one time the Doctor would give his name, so he either wasn't referring to a wedding or they weren't married properly in this alternate reality rush job. Unless the Doctors real name is Lukintomyeye this is not only a dropped story thread, but a major plot hole. Given that this hasn't been mentioned once since I think its just assumed River learnt the name then somehow.
Potential Solution: The Doctor said more than one thing to her.