It seemed to make sense to me that the normally righteous Ned Stark was affected by the war and constant killing and gave in to his feelings, not knowing if he would make it back and all. Didn't even occur to me to start looking for another explanation.
1) Nedd Stark's reticence to talk to John about his mother. Seems to me like it stems from something greater than simple shame, especially since he was a strong man. It seems to me like he might have been driven by the need to protect someone (as he did when he warned Cersei that he was on to her and advised her to flee before he told Robert).
2) The actor who plays John has a similar pale, pasty facial complexion as the actors who play the Targaryen siblings. Could be a simple coincidence though. I'm very visual. I seldom forget a face and I notice these things more than most.
3) John and Dany are very similar in temparement, but they are in completely opposite context. Dany is a legitimate child in a family that was exiled. John is a bastard in a family that is honored (until the end of the first season anyways). Dany is stuck in a desert. John is tied by duty to the northermost, coldest spot of civilisation. John is sworn to a life of celibacy. Dany is force into marriage.
The name of the series is "A Song of Ice and Fire".
I could see John being the central character of the Ice and Dany being the central character of the Fire.
If they were related by blood, it would add an interesting layer to it I think.
4) It would just be cool if after years of having Catelyn shun him for being Nedd's bastard, he could throw it in her face that he's not Nedd's bastard afterall.
5) I just think it would be an interesting plot twist of Nedd's sister had not been an unwilling abductee, but rather had chosen Rhaegar over Robert. Also, according to the reading material, Rhaegar was not stupid so why would he have gone that far in abducting Nedd's sister if she hadn't led him on.
I think Robert, being somewhat of a villain (enforcing tradition over matters of the heart) in this scenario would be in line with the moral ambiguity that permeates the story.