Any ethical problems with dating a former student?
I don't see any inherent ethical problems here: the key word is former student, so there is no present power dynamic, conflict of interest or anything like that.  

However, you should be prepared for those in your department to find out that you are dating a former student, which could create a certain amount of push back.  For instance:


The one year gap between the student being in your course and your romantic relationship will not be apparent to all who know about the relationship.  Even if you tell them, they may not believe it.  Even if neither of you expressed an interest in dating until recently, people may still suspect that you had romantic feelings for one of your students while they were your student.
There is presumably some age differential.  If it is small enough, people will probably ignore it.  If it is large enough, a lot of people will try to figure out "Why is s/he dating him/her?" This will motivate them to find out that your romantic partner is your former student.
If you date more than one former student, people may view you as using your classroom as a hunting ground for future romance.  If this sentiment is held widely, it could make your future students uncomfortable.


I hasten to add that none of these point to any clear ethical lapse or mistake on your part.  In particular, the idea that it is disturbing for a much older (adult) to date a much younger (adult) may be more of a societal taboo/hangup than anything that can be rationally justified.  It is also true that most romantic relationships come with a certain amount of push back, and some kinds of romantic relationships still get a lot of push back for things that many/most of us feel strongly are absolutely unproblematic: e.g. inter-racial relationships, same sex relationships.  (In fact, I am very sorry to say that if your relationship is not inter-racial or same sex, any push back you get will probably be mild compared to that, and if it is, that will increase the push back considerably.)  I recommend weighing the possible costs of such a relationship against the possible benefits.