Character mistake: When Hank is brought to the hospital with gunshot wounds, the ambulance and its two EMTs are met outside by two doctors. One doctor says "Let's get him two grams of oxygen. What's his hemoglobin?" This episode's technical adviser was perhaps away for this scene. How much exactly is two grams of oxygen? Orders for administering oxygen would be given in liters, such as two liters per minute (LPM). The line is presumably meant to be 'two liters of oxygen'. (00:02:25)

Green Light - S3-E4
Continuity mistake: In the scene where Walt is talking to Jesse in Jesse's car, when Jesse pulls out the bag of meth it is in a slide to seal bag. The bag changes between this and a regular ziploc bag from shot to shot. (00:19:30)
Other mistake: Gus is talking to his employee about the twins while writing something on a clipboard. However, he is using the opposite end of the pen and just pretending to write. (00:14:40)

Continuity mistake: Mike Ehrmantraut takes Jesse to a house in the desert. He pulls up behind a dark blue car, which vanishes in the next shot, and then reappears.
Green Light - S3-E4
Visible crew/equipment: When Hank pulls up on the side of the road to answer his phone, the camera crew are reflected in the Jeep's grill. (00:31:00)
Factual error: The final scene of the episode, the cousins are hiding with other migrants amid a farm truck's bales of straw. One of the migrants claims they are in Texas. However, the mountains in the distance are the Manzano Mountains which are just several miles southeast of Albuquerque, more than 200 miles away from the border with Texas and Mexico. The migrant claims he has gone through this route 3 times, so it is unlikely this would simply be a character mistake.
Continuity mistake: When Jessie, Victor and Mike pull into Gus' chicken plant they pull up behind Gus' car, but when they get out the car is gone, and when they start to walk to the building the car is back.
Continuity mistake: When Walt throws the pizza on the roof, it lands 5 rows up from the edge. When the camera cuts to on the garage roof, it's only 3 rows up. Also the amount of topping changes between the angles. (00:34:30)
One Minute - S3-E7
Factual error: As demonstrated in the earlier scene where Leonel shot the truck driver/arms dealer, bulletproof vests do not make the wearer immune to bullets. Bulletproof vests are only designed to stop penetrating injury- they do not counteract the high energy of an impacting round, which can easily break ribs and cause internal injury. When Hank empties Leonel's dropped gun into Marco, Marco is barely staggered despite the fact that he just took five rapidly fired bullets in quick succession to his upper chest. That many hits at such close range in such a small zone would have, at minimum, shattered several of Marco's ribs and potentially punctured one or both of his lungs - both critical and incapacitating injuries on their own. As a result, Marco should have been unable to lift his gun to shoot Hank twice in the chest, much less swing an axe. Additionally, at least one bullet appears to strike Marco's clavicle and upper shoulder- both areas that are not protected by the vest. (00:44:00 - 00:45:00)
Suggested correction: Bullet proof vests disperse the energy of projectile impacts. Bad bruising can result but certainly not broken bones or punctured lungs.
They are not bulletproof vests. The correct name is bullet-resistant vest. Smaller rounds, like a .22 or .25 caliber, can penetrate a vest by going between the protecting fibers because of their smaller size. Also, they are not designed to resist high-powered rifle rounds.

Green Light - S3-E4
Continuity mistake: When Hank is standing between the ATM and the pumps at the gas station, the shadow cast by the roof over the pumps shifts between shots. The shot from away, taken next to the pole with the Indian logo was taken earlier in the day, casting a long shadow. The other shots have a higher sun which has moved by several hours. (00:35:10)

Green Light - S3-E4
Continuity mistake: When Mike gets out to throw Walt into his car the back passenger door is shut but when he throws him in it's open. (00:08:35)
One Minute - S3-E7
Character mistake: When Hank is asked to hand over his gun and badge, he just puts his loaded gun on the table. When, in fact, you would remove the magazine and bullet in the chamber before handing it over.
Green Light - S3-E4
Other mistake: When Gus and Mike meet up in the parking lot, Mike hands Gus a copy of Walter's medical report. When the camera pans down to show the report in Gus' hand, the patient name listed is Jack Test and not Walter White. (00:30:04)

Character mistake: After Walt tries to slap the fly on the paper, he lifts his hand and the math is wrong on one of the sums. He has 6,012 + 7,287 = 13,301. But the actual answer is 13,299. (00:05:45)
Visible crew/equipment: During the shot from the interior of the car of Hank following Jesse, a camera man in a green T-shirt can be seen crouching down on the road to the right of the screen. (00:30:40)

Continuity mistake: When Walt is talking to Saul near the start, we see him unbalance the scales on the table in front of him then lean back. Camera cuts to Saul for a few seconds then shows Walt from behind Saul. In this angle, the scales are now balanced. (00:16:50)
Suggested correction: He could have just been boasting, whilst not actually knowing where he is. He is just a kid after all.
lionhead
Worse than all of that, is the fact that you can't get directly from Mexico into Texas without traversing a river. There are no land routes.
There are no bridges?
lionhead