Is there a problem with defrosting meat on the counter?
A lot of bacteria grows in the range of 40-100°F (4-38°C) (i.e. room temperature). It's definitely not recommended to defrost meat at room temperature. In fact, you are not supposed to leave meat at room temperature for more than an hour. 

However, defrosting in the refrigerator can take a long time and require you to plan at least one day ahead of time. I'm not so good at this, which leads to a safe and fast solution: Defrost meat in a waterproof ziploc bag in cold water. Change the water every 30 minutes until defrosted. The water is a better  conductor of heat than air, so the defrosting is quite fast and the water is cold so there's minimal safety risk.

From the USDA:


  Uh, oh! You're home and forgot to
  defrost something for dinner. You grab
  a package of meat or chicken and use
  hot water to thaw it fast. But is this
  safe? What if you remembered to take
  food out of the freezer, but forgot
  and left the package on the counter
  all day while you were at work?
  
  Neither of these situations are safe,
  and these methods of thawing lead to
  foodborne illness. Food must be kept
  at a safe temperature during "the big
  thaw." Foods are safe indefinitely
  while frozen. However, as soon as food
  begins to defrost and become warmer
  than 40 °F (4 °C), any bacteria that may have
  been present before freezing can begin
  to multiply.
  
  Foods should never be thawed or even
  stored on the counter, or defrosted in
  hot water. Food left above 40 °F
  (unrefrigerated) is not at a safe
  temperature.
  
  Even though the center of the package
  may still be frozen as it thaws on the
  counter, the outer layer of the food
  is in the "Danger Zone," between 40
  and 140 °F (4 °C and 60 °C) – at temperatures where
  bacteria multiply rapidly.
  
  When defrosting frozen foods, it's
  best to plan ahead and thaw food in
  the refrigerator where food will
  remain at a safe, constant temperature
  – 40 °F (4 °C) or below.
  
  There are three safe ways to defrost
  food: in the refrigerator, in cold
  water, and in the microwave.
  
  Refrigerator Thawing Planning ahead is
  the key to this method because of the
  lengthy time involved. A large frozen
  item like a turkey requires at least a
  day (24 hours) for every 5 pounds of
  weight. Even small amounts of frozen
  food -- such as a pound of ground meat
  or boneless chicken breasts -- require
  a full day to thaw. When thawing foods
  in the refrigerator, there are several
  variables to take into account. Some
  areas of an appliance may keep the
  food colder than other areas. Food
  placed in the coldest part will
  require longer defrosting time. Food
  takes longer to thaw in a refrigerator
  set at 35 °F (2 °C) than one set at 40 °F (4 °C).
  
  After thawing in the refrigerator,
  ground meat and poultry should remain
  useable for an additional day or two
  before cooking; red meat, 3 to 5 days.
  Foods defrosted in the refrigerator
  can be refrozen without cooking,
  although there may be some loss of
  quality.
  
  Cold Water Thawing
  
  This method is faster than
  refrigerator thawing but requires more
  attention. The food must be in a
  leak-proof package or plastic bag. If
  the bag leaks, bacteria from the air
  or surrounding environment could be
  introduced into the food. Also, meat
  tissue can also absorb water like a
  sponge, resulting in a watery product.
  
  The bag should be submerged in cold
  tap water, changing the water every 30
  minutes so it continues to thaw. Small
  packages of meat or poultry – about a
  pound – may defrost in an hour or
  less. A 3- to 4-pound package may take
  2 to 3 hours. For whole turkeys,
  estimate about 30 minutes per pound.
  If thawed completely, the food must be
  cooked immediately. 
  
  Foods thawed by the cold water method
  should be cooked before refreezing.