I would see a need to constantly keep a secret. And like most teenagers who try to keep stuff from their parents, the folks will eventually find out.
I would also see a relationship that would be completely based on physical attraction. This is fine for a beginning, but it should lead into a friendship and a partnership that shares in the business of a life together. This relationship is shaping up to be only about the physical when Romeo and Juliet can find times to meet if they intend to keep their secret. Purely physical relationships only last so long because they become predictable and no longer as exciting as they were in the beginning.
This also begs the question about marrying ages. When Romeo and Juliet's parents do encourage a marriage to other folks, what is the Friar going to do then? Let them know that he a holy man has kept a secret from them? Would he marry the two to others and encourage polygamy? Friar has a lot to think about.
As most married people can tell you, in-laws can be a source of tension for a married couple. In the case of Romeo and Juliet, you would think that this would be ten times worse than usual.
In their case, either one of them is going to have to totally give up their family, or they are going to have huge fights about it. What happens if they have kids and Juliet's mom wants to come over and see the kids? Will Romeo allow it? When it comes time for the baptism, who will be godparents? Will the two families be able to hang out together?
So, the problem I see is just one of the families -- they will probably continue to hate each other, and that will cause problems for Romeo and Juliet.
Any answer to a question like the one you ask is, of course, speculation. That said, I'll try to at least base my answer on evidence from the play.
I suspect Friar Lawrence, in addition to the problem of in-laws mentioned above, might foresee two problems.
First, Romeo's sudden change of heart in act one of Romeo and Juliet is problematic. One minute he's depressed over Rosaline, and the next he's elated over Juliet. What guarantee exists that that won't happen again?
Second, and this is related to the first, is the impulsive nature of both Romeo and Juliet. Impulsiveness does not necessarily lend itself to strong relationships. With both of them being so impulsive, who knows what trouble they will get themselves into, together or separately?
For whatever it's worth, I suggest those are two problems Friar Lawrence, or anyone, might foresee in the marriage of Romeo and Juliet.