In regards to the whole Targaryen thing:
1. People would have to accept Northern marriage rituals to accept you as a trueborn Targaryen. Aka, the faith ain't buying it.
2. They'd have to believe you and Arthur Dayne when you reveal this. Unless people who know Dayne are present, this could be a hard sell.
3. You would have to accept (or recognize) Rhaegar's interpretation of events and accept the fact that you're claiming the throne on the basis of your mother being raped by the crown prince.
Looking at 1 and 2, if we are going to take westeros we're probably going to need something big to get people on our side, be it a dragon or a really powerul shout. Otherwise getting support will be difficult.
As for 3, the only way I can see Jon justifying it is if it is done to save the realm from a really bad king. Luckily, Joffery will deal with that for us.