The main weakness was a large helot or slave population. In 725, the Spartans needed fertile land to feed a dramatically growing population. To fix this problem the Spartans marched over the Taygetus Mountains and seized all the territory of their neighbour, Messenia. The Spartans chose to seize this land because the Messenians had settled over very fertile land, and the Spartans then found themselves with more than enough land to support themselves and their newly conquered people. The Messenians did not appreciate the loss of their liberty and freedom so the Messenians obtained an alliance with the city-state of Argos, and revolted in 640 BC. Not only did the Messenians come close to victory, they also came close to razing the city of Sparta itself to the ground. Throughout its history, the Spartans had considerable problems with helot rebellions. This was what transformed Sparta into what it is known as today.
The Messenians were turned into agricultural slaves called helots. A description of their lives as a serf (a person who is bound to the land and owned by the feudal lord) is that they worked in small plots of land on estates owned by a Spartan. Parts of their produce went to the master of the estate, and the remainder went to the helot (serf) farmer and his family. There is no question that the life of the helots was a miserable one, the labour was long and hard and the helots always lived right on the border of subsistence.
In the 6th Century BC, the Spartans began to set their military sights on neighbouring states. However, when they conquered their neighbour Tegea, not wanting to further increase an already great nu0mber of slaves, they negotiated with their defeated enemies rather than annexing their land and people. They demanded an alliance of sorts. Tegea would follow Sparta in all its foreign relationships, including wars, and would supply Sparta with a fixed amount of soldiers and equipment. In exchange, the Tegeans could remain an independent state. This was a brilliant diplomatic move and with this method in hand, the Sparta formed alliances with a huge number of states in the southern part of Greece (called the Peloponnese), and had become the major power in Greece when the Persians invaded in 490 BC.
The military and the city-state became the centre of Spartan existence. The state determined whether children, both male and female, were strong when they were born; weak or sick infants were left in the hills to die of exposure. Exposing weak or sickly children was a common practice in the Greek world, but Sparta institutionalised it as a state practice rather than a domestic activity.
At the age of seven, every male Spartan was sent to a military and athletic school. These schools taught toughness, discipline, endurance of pain (often severe pain), and survival skills. At the age of 20, the Spartan became a soldier. The Spartan soldier spent his life with his fellow soldiers and lived in the barracks and ate all his meals with his fellow soldiers. A Spartan soldier would also marry, but would not live with his wife. Only at the age of thirty, did the Spartan become an "equal," and was allowed to live in his own house with his own family, although he continued to serve in the military. Military service ended at the age of sixty. Each Spartan soldier was granted a piece of land, which he almost certainly never saw and of course, was farmed by the helots.
The Spartans are probably the most skilled warriors in Ancient History, and their tactics were brutal but extremely effective (the Phalanx formation, etc). Sources said they that had a lot of passion and will to fight that would make anyone tremble in a matter of seconds. It could also be said that the Spartans had the spirit of Heracles.
http://wsu.edu/~dee/GREECE/SPARTA.HTM
http://www.bbc.co.uk/dna/h2g2/A9565437
http://wsu.edu/~dee/GREECE/SPARTA.HTM
http://www.crystalinks.com/greekeducation.html
http://wsu.edu/~dee/GREECE/SPARTA.HTM