There are two major hindrances in problem solving: mental sets and functional fixedness. A mental set is the tendency people have to deal with a new problem in the same way that they have dealt with old ones. A person trapped into old habits and sterotypes turns a problem into an extremely difficult puzzel, whereas someone with flexibility and creative thinking skills finds the easy route. An example of a mental set is this problem:

Q: There is a butcher that works in a meat shop: he is 5 foot 10 inches tall, his waist line is 34 inches and he is of medium build. What does he weigh?
A: Meat

The problem solver sees the word "weigh" and thinks "weight" (of the butcher), assuming that this will be a problem which will result in a numeric answer. This assumption is aided by the amount of numbers involved in the question (5 foot 10, 34 inches), causing an inflexible problem solver to fall into a mental set.
The other major hindrance in problem solving is known as functional fixedness. This refers to the problems people have finding a new use for a familiar object. The organization "Odyssey of the Mind" frequently forces its members to face this hindrance by presenting them with an object (say, a pencil) and awarding points for the most creative use for that object. But problems resulting from functional fixedness are not merely elementary. When the Apollo 13 ran out of Carbon Dioxide filters, engineers back at NASA had to come up with a way to make square filters fit into circular holes. With limited resources to work with, these geniuses found themselves forced to see every scrap of material under a new light.