During the gunfight at the first of the episode, Rick is shot just below his left shoulder, in the back. After he awakens in the hospital, and thereafter, he is shown with a bandage over his lower left abdomen, and there isn't a scratch on his back.
When Rick wakes up in Morgan's house, there are no marks or wounds on his face from where Duane hit him with the shovel.
As Rick crawls under the tank there's a green blanket in some shots and not in others.
When Rick slides under the tank for safety there is a brown blanket to his left. In the reverse shot of him from under the tank the blanket is missing.
Rick tells Leon to make sure he has a round in the chamber of his gun and the safety off. Leon then chambers a round and makes a thumb motion on the side of his pistol as if flipping a safety switch, and the sound of a switch is heard. However, Leon's gun is a Glock. Glocks do not have external safeties. (The small lever that Leon swipes his thumb over is actually the slide lock.)
Rick has been laying in a hospital bed for months when he finally wakes up. His muscles should be atrophied and useless, and he should be covered in bed sores as no one has been moving or cleaning him for at least a couple weeks. Additionally his vocal chords would also not function immediately.
The police leave someone to pull stop sticks off the road so the cars following can pass safely. There is no conceivable reason for stop sticks to cause a car to flip over. They are designed to slowly deflate the tires to prevent loss of control. The point is to slow the fleeing car, not make it crash.
Inside the tank, the lights and radio are on, which would drain the batteries in a few hours.
During the car chase and shootout scene in the first episode, Rick tells one of the deputies to make sure he has his gun's safety off. The gun he has is a Glock, which does not have a safety.
When Rick finally makes his way out of the hospital, and is standing in the courtyard surrounded by corpses, the building he is supposed to have just left has clearly been abandoned for some years and is partially decaying. The building is revealed to have been partially blown up by the military in a Flashback scene in "TS-19" which accounts for its dilapidated and damaged appearance.
When Rick is on the horse in the city and he sees the reflection of a helicopter, he runs into a mass of zombies. Look closely and you will supposedly see a clean non-zombie guy drinking from a cup in the back left of the zombie mass. However, if you look real closely in the zombie mass in the previous shot before the horse jerks back and the shot after when the hoard of zombies start chasing Rick you will see the same "non-zombie guy" on the left and his face indicating he is actually one of the zombies. You can tell it's the same guy because of the shirt/dark sleeveless leather jacket he's wearing.
When Rick awakes in the hospital you can see that his IV bag is empty. Blood backs up into IV lines when a bag is empty because it forms a vacuum. Rick's lines are blood free.
The tank which Rick hides in is a Cheiftain Mk10. It is a British Army tank designated FV4201, manufactured by Leyland and used by the British Army between 1966 and 1995. The tank in the episode (along with those seen outside CDC later in the "Wildfire" episode) are all painted tan and feature the inverted black "V" which was used to identify Coalition troops during the First Gulf War. This model of tank was never in service with the American Army and as such it would be highly unlikely to see four of them abandoned in Atlanta as depicted.
The M1 Abrams tank is actually one of the few tanks without a "belly hatch." The "M1 Abrams" in the show is actually a different tank mocked up with fake body panels to pose as an modern Abrams.
During the shootout following the car chase you can see elbow pad on the first gunman as he falls after being shot.
At the very end of the first episode after revealing they are alone and everyone is dead, the camera pulls back and reveals busy city traffic on the horizon moving.
The radio in the tank is the AN/VRC-12 series, which has been obsolete since at least 2000.
At 12:11 You Can See The Second Gunman's Squib Vest Underneath His Shirt. A Squib Vest Is Worn To Protect Actors From Burns.
Rick is supposedly going south on I-85 going into Atlanta, but that is not the skyline of Atlanta you would see if you were heading south. The skyline is from Freedom Parkway, facing West.
Rick was supposedly in a coma for well over a month. This is impossible as he would have died within 3-5 days without water or IV fluids. It was stated the that the utilities have been off for a month meaning he had no way to get either.
With the slow spread of the "virus" it would have been easily controlled at the start. Since it takes hours for a person to change.
Right before Rick finds the horse he finds a pickup, but the keys weren't in it. If he had gone inside the house and searched it he would have found the keys right away as they were hanging on a hook just inside the front door, they can be seen while Rick is knocking on the door.
At the beginning of the episode the deputies establish their roadblock incorrectly. The patrol cars should have been angled so that they point in the direction of traffic. That way if the fugitive tries to run the roadblock the cars will be pushed to the side of the road instead of crushing the officers between them.