Adults generally see teenager's problems as being very transitory and unimportant in the grand scheme of things. When adults think of teenage problems they think of things like curfew, teenage heartbreak, friendship drama, school issues, and the latest fashions. Adults think of adult problems being things like financial problems, marital issues, losing a job, health concerns, and family issues. Obviously, losing a job is a much bigger problem than wanting to stay out later on a Saturday night.
Where I think adults make a mistake is in assuming teenage problems are less important than adult's because they seem unimportant to the adult. Regardless of the problem, it is a real problem to the teenager experiencing it. And some problems are serious. Teenagers are forced into dealing with adult problems more frequently than they should be. But even if the problem is just a "teenage problem", it is still serious to the teenager and they often lack the experience and power to deal with it effectively.
When an adult is faced with a problem, there is often something they can do about it. If they are in danger of losing their home they can call the mortgage company, they can get a second job - they have some power in the situation and they have some experience and knowledge in how to handle it. When a teen is faced with a problem they often have no power to exert any force over their situation and they frequently lack the experience to formulate a plan of action. They also do not have the emotional maturity to view the situation objectively.
So while I do not think that teenagers have more problems than adults do, I think they often lack the skills to deal with their problems in the same way adults do. This makes their problems seem just as real and sometimes more difficult than those that face adults.