Bright Light
The biggest disadvantage of a laser sight is that the beam -- particularly with red lasers (green lasers are not as bad) -- may be difficult to see in daylight or brightly lit conditions. High ambient light makes it easy to lose sight of the laser beam.
Position Giveaway
Using a laser sight generates a light beam directly from your position, which gives away your location to anyone who can detect the beam's origin. This can be detrimental if you are attempting to conceal your position.
Dependence on Batteries
Laser sights rely on batteries for power, which is fine provided that the batteries have power. However, if the batteries are low on power, you could lose your sight without warning as the batteries die.