(at around 25 mins) A camera is seen filming the alien despite all electronics being disabled earlier in the film.
When Ray, Rachel, and Robbie run into the concrete utility room to escape the fireball from the crashing plane, Ray has to struggle to push the door closed against the flames. But in the morning, exiting the room, he pushes it open. He should have pulled it open to exit the room.
After the lightning storm, Ray exits the front of the house to find all the cars outside are disabled. Apart from the very first two seen, behind him at the bottom of the stairs - they still have their rear lights on.
Before the first alien tripod comes out of the ground, a circular portion of the ground turns to rubble and then twists counter clockwise. Ray looks at the church and sees the front of it twisting counter clockwise, but then looks down at the ground by his feet (in the same shot), and the ground is twisting clockwise.
After Ray throws the baseball and breaks a window, the following shot is from the inside of the house and through the broken hole in the window. The shape of the broken window from outside doesn't match the shape from the inside.
After the 747 crash they came out of the house and jumped into the van they parked outside before and leave. Due to the closeness of the crash, the van would have been obliterated.
When they're exiting the home where the jumbo jet crashed, the cockpit window is broken with a hole in it. Cockpit windows do not break like windows in homes. They are in fact multiple layers of various materials including special glass, heating elements, bonding materials, etc, and when they break, they "spiderweb" into many, many small pieces. The window in this scene appeared to be a single pane of glass that looked like it had a rock thrown through it.
The Train (Acela) streams by while on fire. All trains have a "deadman" switch. They come to a full emergency stop if the engineer is incapacitated (as he/she would be if on fire).
As the Hudson-Athens ferry capsizes, Tom Cruise and his two children are almost crushed as a car slides off the ferry and quickly sinks, going straight to the bottom. We see that this sedan-style car has people in it, and that the windows are closed, so the passenger compartment has not yet flooded. It is still full of air. A sedan full of air would not quickly sink. It would briefly float on the surface, then slowly submerge as the passenger compartment floods.
If a large jumbo jet crashes into a house, and the house catches fire just as it it did as everyone got into the concrete utility room, it would have burned considerably more than shown. The basement had some charring, but there were plenty of clothes and other flammable debris scattered around, unburnt after the fireball supposedly engulfed the basement.
When Rachel tells Ray she won third place in walk/trot/canter, it appears that she is holding a green ribbon. Third place is gold/yellow for equestrian events and green is sixth place. Earlier in the film, at about the 12 min. mark, when they order food, Rachel has the ribbon laying on her leg and as the camera pans across it, you can see that it is gold and has a horses head on it. The ribbon appears to be green later in the film as it has become dirtied while they are on the run.
After Ray throws the slice of bread at the window from the inside, it appears to be thrown from the outside. In fact you see the reflection of Ray in the window, shot from the inside.
It's a special Hollywood EMP that disables only the electronic equipment that the filmmakers want it to. While "technically" it's a factual mistake that, for instance, the camcorder is still working, it was clearly a deliberate decision by the filmmakers. We also only have a TV reporter's word for it that it's an "EMP" anyway, so it could be an alien weapon of which we know nothing.
Near the end of the film, a group of soldiers attack an alien drone with a Javelin shoulder-fired missile launcher. The firing effect in the film has a dramatic backblast complete with flames shooting out of the missile tube. The actual Javelin has a "soft-launch" feature where the missile weakly pops out of the tube and travels a certain distance before the main rocket motor ignites. It was designed to help mask the gunner's firing position.
When driving up to Boston in the minivan, the gear selector lever is in the park position.
When Ray throws the baseball and Robbie lets it go past him and through the window, Ray does not actually have anything in his hand when he throws the ball.
When Ray comes out of the basement after the plane crashed near the house you can see most of the walls have been blown away by the explosion. Most of the items inside the house thought (photos, lamp) are still standing upright in their original position without being burned.
When Rachel goes running up to her mom and step-fathers house at night, the door is left open for them miraculously when they were on a vacation to Boston.
When Rachel was channel surfing at Ray's place, she finally decides to watch SpongeBob SquarePants (1999). However, the audio is unsynchronized with what is happening.
When Robbie returns from the downtown area where the lightning struck 26 times, you can hear him talking about it to Ray; you can't see his face, but when the camera zooms in on him, his mouth isn't moving.
When the aliens visit the basement, one of them spins a wheel on a bicycle hanging on the wall. It clicks as it spins, indicating it has a freehub, even though it was the front wheel. Only rear wheels have freehubs.
When Ray is leaving his ex-wife's house after the tripods destroy it, you can see a crew member lean back behind the jet engine as the camera pans to the right.
While driving down the interstate the camera pans back and you can see red flashing lights on the opposite lanes. Presumably these are state troopers blocking the interstate for filming.
In Mary Ann's kitchen, just as Ray comments, "Ok, well you hungry? I'll get you some food," the clear reflection of a male crew-member moving around is visible in the glass window behind Ray. Then just as he says, "This is ketchup and mustard," another older male crew-member is visible directly in front of Rachel's reflection.
As Ray begins to leave the house after the plane crash, stopping to pick up Robbie, the reflection of the camera operator is visible between the passenger and sliding side doors.
In the ferry boat scene, fleeing crowds are back lit by floodlights placed off the main street, not by the lights of the approaching tripods.
When Ray arrives to his ex-wife's house, you can see a flat forest behind all the houses in the street. After the Jumbo jet has crashed you can see a little hill behind the destroyed houses.
After the Bayonne Bridge blows up, you see them driving on "440/West Shore Expressway". This is on the other side of the bridge in Staten Island so this is not possible.
Passenger trains along the Hudson River run along the east bank of the Hudson, not the west bank, where the ferry was departing.
When the tripod emerges Ray hides behind a building on Polk Street, but when he comes out he is on Van Buren Street. Then he is back on Polk Street coming out of the store.
The mountains where the second half of the movie takes place are nowhere near New Jersey (filmed in the mountains of Central Virginia).
In the part where the jet crashes into the house, it should have destroyed everything in sight, but the mini-van Ray was driving afterwards was unharmed.
If the theory that the tripods had been place/buried long before the aliens arrived to occupy them, then it would seem plausible at some point that at least one would have been discovered through construction or utility work.
When Ray returns home after witnessing the first tripod emerge, his children ask what's going on as if they haven't seen or heard anything. With the level of destruction caused (and the fact that their TVs are off due to the power being out), they would have had to have heard or seen some activity, since Ray had to live within walking distance of the affected area, because he wasn't driving.
When Ray comes home after the Aliens first appear, he falls down in front of a refrigerator. The boom mic is visible at the top of the screen for a few seconds in that shot.
When Ray and Ogilvy play tug-of-war with the gun, as the aliens rummage around the cellar, Ogilvy finally pulls it away from Ray. In the next close-up of Ogilvy and his gun, the boom mic dips down for a moment, but it's gone in Ogilvy's next close-up.
Right after the appearance of the first tripod, Manny the Mechanic, having just repaired the minivan that Ray, Robbie, and Rachel use to escape in, seems completely oblivious to the chaos and panicking of people going on around him in the neighborhood.
The Ferry Boat Captain is wearing a U.S. Navy officer's cap, not that of a Merchant Marine officer.
In the beginning, when the first hole starts to crack, Ray is smiling/laughing as he backs away.