Continuity mistake: When Rachel runs to her mom, in Boston, in the side shot of Mary Ann she's already gone down the stairs and crossed the sidewalk towards her daughter, yet in the next shot it's Rachel who crosses the sidewalk towards her mom, who is still up at the center of the stairs. (01:47:05)
Continuity mistake: In Boston, when Mary Ann lifts Rachel, she holds her daughter then turns to face Ray and says, "Thank you." Behind them, up the stairs, the left front door is already wide open, yet in the next shot both doors are closed until her parents dramatically open them. (01:47:30)
Continuity mistake: In the end of the movie before his son runs to him Tom Cruise is standing in the sunlight. In the next shot there is no direct sunlight. (01:48:00)
Continuity mistake: When Ray is outside at the beginning of the movie during the lightning storm, he says to himself that the wind is moving in the direction of the storm. Yet when he calls to Rachel to come outside and take a look, her hair is blowing away from her face, in the opposite direction it should be blowing.
Continuity mistake: Just before the first alien tripod breaks free from the ground and cracks are appearing in the street, the front of the church cracks, and rocks away from its second half. In that shot, in the view from behind Ray, he places his right foot on the curb, while his left foot is on the road. In the next shot facing Ray, both his feet are on the curb.
Continuity mistake: In the scene when the intersection is rotating, the camera is aimed up towards the church and starts to pan down. Tom Cruise runs into the scene and gets behind a car. The movement of the church shows the intersection is turning counter-clockwise but as it pans to the ground, the intersection is turning clockwise.
Continuity mistake: When Ray and the kids are driving down the freeway, there are several cars stopped randomly so they have to swerve a lot. But when it shows them inside the car, talking, they are driving perfectly straight. When it shows them from the outside again, the random cars are back and they start swerving again.
Continuity mistake: Ray and Rachel are about to walk down into the basement at Harlan's house, the door on the right of the bulkhead is open and the door on the left is closed. In the view from the basement you will notice that the door on the left is open and the door on the right is closed.

Continuity mistake: When the tripod is taken down, the lights are flickered out on it. But in a couple of scenes later, the lights are working again on the tripod, right before the alien crawls out of the hatch.
Continuity mistake: This movie has to take place over at least 4 to 7 days for them to walk from New York to Boston. When they arrive in Boston, he has absolutely no facial hair growth.
Continuity mistake: When in their home basement, when the lightning starts they take shelter in the utility room and the door is a cross and bible style door that opens out. When Ray shuts the door against the fire he pushes it closed instead of pulling it, and it is a plain flat door. If there were two separate doors the fire wouldn't be burning through the still intact cross and bible door that Ray opens properly in daylight.
Continuity mistake: When they arrive at the ferry port a man throws something at the windshield which hits the top, and the screen around it shatters. In the following shot the car hits a pole and the damage has moved to the middle, and it's now a perfect hole.
Continuity mistake: When the movie ends, Rachel runs to hug her mother and a strong wind blows large amounts of leaves a meter up. A frame later, from a different angle, the wind is milder and the leaves barely move.
Continuity mistake: Ray runs out of the house looking for Rachel and moves away some weeds blocking the door. When the angle changes the door is spotless.
Continuity mistake: When Rachel is watching the floating corpses in the river, the shots alternate back and forth between a wide angle where she is standing still and wind is not blowing, to a close-up where she is sobbing, moving her shoulders up and down rhythmically and her hair is moving rapidly.
Continuity mistake: When the movie ends and Ray meets his family, the street keeps swapping from sunny to shadowy back and forth.
Chosen answer: In the original George Pal version they were Martians and the reasoning for what they were doing was never explained. In this version, it's never explained where they come from, but their mission is simple, to eradicate human life from Earth, and use our bodies to fertilise the planet, probably so that they can colonise the planet for themselves.
GalahadFairlight
If it was to eradicate us they could have done that millions of years back, why now, so that doesn't add up.
You want to grow the substance (people) that grows your food source before using it. If they waited too much longer, they'd have a harder time because we'd have the technology to fight them back.
The reason which was apparently provided by Wells was that Mars was dying by lack of natural resources and that Martians needed a new home and food source.
They were waiting until the population grew large enough to sustain terraforming efforts. As they used our bodily fluids seemingly as a primary material for their terraforming.
It's an assumption that they could have eradicated us millions of years ago (which by the way would be long before we even existed). Maybe they didn't have the ability to transport themselves, only the machines. Maybe the original aliens all died. Lots of other options why they couldn't have done it.
They probably needed to wait for us to produce enough humans to use as fertilizer. Doesn't make sense to try to use several million bodies as fertilizer back then vs now with billions of people.