It also helps to be on the side of the plane facing south or west.
Wrong. The 24 to 32 GPS satellites are spread equally around earth, so that at least 6 satellites are visible at any one point almost everywhere on earth. These are not your normal TV network satellites, so they're not concentrated to the south or west of most continental US positions. They will be south of you, north of you, west of you, and east of you.
It helps to be on the side of the plane with a most direct LOS (Line of Sight) to as many satellites as possible at any given time, but that varies with where you are.
I read somewhere that the GPS in the Droid resolves position based on input from a data (3G or WiFi) source, it's not a full-blown, independent GPS receiver. That could certainly be wrong, but that's what I recall reading.
Also incorrect. Specifically, the location unit in the Droid is an A-GPS, or Assisted GPS. What this means is that the GPS unit in the phone is a full blown, independent GPS unit, capable of calculating it's location by no other means but GPS satellites, if need be. However, it's not a /good/ GPS unit, the antenna for instance is small to say the least. So if the phone was to determine it's location using nothing but GPS it can take a long time, indeed as long as 20 minutes. So to help speed this up the phone also uses cell phone tower triangulation to secure a rough fix, then feeds this to the GPS unit, which can then fine tune this fix using the GPS signals.
This is why sometimes when you first open your map you'll see a rough estimate of where you are, though within seconds to a minute you'll exactly where you are.
Speed and altitude does not have any impact on being able to utilize GPS, it's the primary navigation system we use on the jet I fly. However, like others mentioned, the antenna(s) are on the outside of the fuselage, on the top, under a thin plastic cover. The reason you will have problems locking on when sitting in the cabin of an airliner is the relationship between the thickness of the hull of the aircraft and the strength (or rather, lack thereof) of the GPS signal; Each GPS satellite transmitter transmits it's signals with no more power than that of an average car headlight..
With that in mind hopefully it'll make more sense why you're having problems locking on any time you're inside a building, under a roof or in an airplane.