Bart Sibrel's video argues that this television footage was made in low Earth orbit, rather than on the way to the Moon. The images of Earth, he claims, are either black cardboard with a round hole cut out, or a transparency. Note right there that these are mutually exclusive - If he doesn't know, then he is just guessing without evidence. In fact, there is evidence, but it doesn't support either of Sibrel's conjectures.
Apollohoax.com member "PhantomWolf" has already pointed out that the behavior of the Earth images is in no way consistent with something attached to the window itself. I've been looking at the content of the Earth images.
As PhantomWolf said, in the first day-and-a-half of the mission there were three live television transmissions from the Apollo 11 spacecraft, which showed the Earth out the window. At about the same time as each of these transmissions, the astronauts also photographed the Earth using a 70mm Hasselblad camera. These provide exceptionally high-resolution images. Here are frame grabs from each of the three transmissions, with a photograph taken at about the same time for comparison.
Note that the cloud patterns match:
(Images courtesy of Earth Sciences and Image Analysis Laboratory, NASA Johnson Space Center.)
As you can readily see, the photographs show the whole planet with spherical shading rather than just a portion. In the hi-res versions you can see features - most of North America appears in all three images. Were these images prepared in advance and hung out the window to stage a hoax? This is a testable question. If this was an authentic transmission, and the TV transmission was going out live, and the hi-res photographs match the TV images, then the weather patterns visible in the photographs must match the local weather measured across the country at the time the images were taken.
So, do the weather patterns match?
Here is the precipitation map for the continental United States on July 17, 1969 (the date of the 2nd & 3rd transmissions):
Here is a cropped version of a hi-res scan of AS11-36-5373 showing North America:
The features I highlighted are:
A.) Summer monsoons over Arizona
B.) Rain over the Midwest
C.) Rain over western Canada
D.) A cold front moving down from Canada into the northcentral and northeastern US.
E.) Summer thunderstorms over the southeastern states
F.) A separate storm cell over southern Florida
G.) A separate storm system over the Texas gulf coast.
The features match. The photographs and the live video from the spacecraft were definitely taken on the afternoon of July 17, 1969 and both cameras were a long, long way from low Earth orbit.