This is a field growing by leaps and bounds. If you have any interest in international economic law (in itself, a field moving very quickly), then intellectual property rights issues are a central topic. Questions here can include the following: Do inventors have an inherent right to copyright? Should states in the EU or the U.S. place legal sanctions on states that do not respect intellectual property? What is the legal history of copyright law relative to international trade? All of these are challenges, but little in international law is more controversial and more relevant to trade agreements, free trade and international economics.
For more domestic concerns, age of consent rules are under challenge. The idea here is that killers who are 15 or 16 years of age, given the prevailing culture, should be tried as adults. This has a long and interesting paper trail that is easily accessible in any good law library. Basic questions can include the interplay of culture and music with "growing up too fast." For example, 15-year-olds exposed to many forms of music, ideas and education have an understanding of crime that demands they be tried as adults. This may not have been as relevant 100 years ago. There is an interplay between law, ideas and culture that alter how youngsters approach crime.
For those interested in business law, the idea of limited companies and the protections they afford is a topic worth considering. A limited firm is one where a shareholder cannot be sued for personal money, only money invested in the firm. Since the firm is a legal person, its "holdings" derive from investment cash. But given the existence of widespread corporate malfeasance, the question of expanding the ability of prosecutors to go after personal income for major investors might work even when only firm policies are at issue.
This is an old one. A penumbra is a 'shadow' of a statute, something implied by a statute that expands that statute's power. The most infamous example of this is Roe v. Wade, that stretched the "right to privacy" (itself a penumbra) into protections for legal abortion. This example is a penumbra that itself was brought to create another one. What is the legal basis for this? Is it legitimate? What is the common law foundation here? Even in the early American republic, constitutional clauses like "necessary and proper" were major sticking points for the founders. The "necessary and proper" clause is an early example of a penumbra, since it is meant to give powers to the state "necessary and proper" to its duties. Many founders thought this was a means of giving the federal government far too much power.