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Fridge Brilliance: In the book it's mentioned that for all the technology the Martians never seem to have invented something as simple as the wheel, what are the Martians so fascinated by when we see them outside their tripods? A bicycle wheel.
Why does the Martian's weapon leave clothing intact? Its an highly-focused enhanced radiation weapon similar to a neutron bomb, which is designed to wipe out enemies soldiers but leave their infrastructure relatively intact. This is why it dessicates humans into ash but less of an effect on clothing (and armour). Similarly, it also demonstrates similarlities to a neutron bomb's having some concussive force, in the way that it impacts objects. It isn't a "heat ray" at all, as throughout the films, we never see it ignite objects, the only fires seen are clearly caused by explosions from other sources.
When the aliens go through Ogilvy's basement, they all look at a picture of what's presumed to be Ogilvy's deceased daughter. Notice that they all look at it the wrong way (as in, never viewing it upright). Common from something that's never seen a photograph before.
Fridge Logic: The aliens somehow get gigantic war-vehicles to come out of the ground. See the Headscratchers page for more in-depth discussion.