In the movie Lindberg with James Stewart, a fly rides along in the
cockpit of the plane.  Does the planes weight change (by the weight of
the fly) depending on whether the fly is flying around within the
cockpit or if it has landed on something within the plane?  Why?

From a discussion of a similar problem, involving a pigeon rather than a fly:

"The pigeon takes off and flies around the cabin. What does the plane
weigh? Exactly the same. On average, the pigeon must exert one pound
of downward force on the cabin air to keep itself aloft, and the cabin
air in turn presses down on the airplane."

http://www.straightdope.com/classics/a3_144.html

I believe the comment made by pinkfreud is partly correct and partly
incorrect. It is correct becuase it is the right answer but for the
wrong wrong reason. The answer should not make reference to cabin air
pressure as this has no impact on the weight of the plane (or its
mass).

The question is slightly misleading as it refers to weight. If the
plane is flying level then it is weightless. The upward force of the
wings is matched exactly by the downward acceleation of the aircraft
due to gravity. It has no weight.

If the fly takes of, flys and land in the cockpit, the fly is only
changing the internal forces on the fly within the cockpit. It has no
effect on the external forces of the aircraft as the cockpit is
sealed.

Perhaps the question should consider the mass of the air plane rather
than weight. The mass stays constant no matter what the airplane is
doing or what the fly is doing in the cockpit. The mass is the sum of
the mass of plane and its contents including the fly and the air
surrounding the fly. It matters not whether the fly is crawling on the
cabin floor or is flying in the air, the mass of the plane includes
the fly and the air around the fly. By taking off, the fly only
adjusts the internal air pressure not the mass of the air.

One last consideration. If the fly suddenly materialised [impossible
but hypothethetical) in mid air in the plane, the plane mass would
increase by the mass of the fly. Why? The fly displaces the air around
it creating less air volume but more pressurised air - the mass of the
air would remain identical. The weight then changes only by the fly
not by the air around it.

pinkfreud is correct. The other person's answer makes no sense.

Perhaps you could elaborate which bit of my answer you believe not make any sense.
To make it easier, I will repeat all my statements in simple for, then
you can pick and choose:

1) Pinkfreud has the correct answer
2) Pinkfreuds explanation for that answer is incorrect
3) The question is better expressed as mass rather than weight
4) The plane is weightless when flying in equilibrium
5) The fly (in a sealed cockpit) can only affect the internal air
pressures within the cockpit or the stresses on the aircraft body
6) The fly (In a sealed cockpit) can not influence the upwards or
downwards forces on the airplane itself
7) The existance of the fly effects the mass of the aircraft. The mass
remains constant whether the fly is crawling or flying in the cockpit.

If the cockpit is NOT sealed, the fly will certainly effect the weight
of the aircraft by creating repulsion forces by the air being expeled
from the aircraft under pressure as the fly beats its wings.

I leave you with a question to illustrate my point.

If a man in a sail boat blows into the sail with a pair of bellows,
does the boat move? What if he pushes against the mast, does the boat
move? In both cases the answer is no, all he does is creates stress in
the structure of the boat, but no force moving the boat in any
direction. This is the same effect of tthe fly beating its wings in
the sealed cockpit, it can not effect the forces on the aircraft with
repect to the outside world (hence, no effect on the weight).

Are you happy with the distinction between mass and weight?

OK, I withdraw my previous comment. I have thought about it a little
more and it turns out I am an arse.

Pinkfreud-ga is correct.

A complete answer must take air pressure into account.

Anything which flies must support itself by generating a pressure
difference between its lower and upper surfaces.  Hence the air
pressure below a flying object is greater than that above it.

It follows that the *average* air pressure (extending right down to
the floor) below the flying object is greater than the average
pressure above it.

Converting pressure into force withing a sealed container, it follows
that the consequent downward force acting on the bottom of the
container is greater that the upward force acting on the top of the
container.

As an example of this, if I lie flat on the ground and a hovercraft
passes over me, I experience an increase in the pressue of air.  It's
the same effect when a fly buzzes overhead inside an aircraft, or
anywhere-else.

Indeed air pressure plays a roll. As the fly takes off the plane
actuialy would "weigh" slightly more becuase the energy the fly is
using to push itself up is also pushing the plane down an equal
amount. (If the fly were in flight like an airplane or a bird flies
then it would be lift, not downward thrust, that kept the fly aloft)
That would have a different effect.

Sorry... i missed a few sentences in my answer.

"Because the fly is converting potential energy of chemecals in it's
body into kenetic energy of creating downforce with it's wings, it
will push the plane down slightly."

Perhaps the answer only involves the difference between the weight of
the fly and the weight of the volume of air displaced by the volume of
the fly.

The gedanken experiment posed by antipodean_manc regarding the man in
a sail boat is interesting. However, the assertion that the boat would
not move if the man blows into the sail with a bellows is incorrect.
The boat would move, albeit very inefficiently. (Note that sail boats
do not move because the wind fully inflates a sail, but rather the
sail acts as an airfoil and lift is generated in the horizontal plane.
This lift is what propels the sail boat through the water.) The
bellows would push air into the sail. Pushing the air into the sail
exerts a pressure on the sail, and therefore a small force, since the
sail has a surface area. Thus, the force would push a little bit on
the sail, and the boat would move a little bit. This is no different
that if a fan were used to push air into the sail. It would act the
same way and the boat would move. If a force is produced, by a man
with a bellows or an engine, then there must be an opposite reaction
to that force.