
Visible crew/equipment: At the very end of the episode, right after he tells Jesse how he used the red phosphorus to kill the gunmen, Walt leans down to vomit. You can see his microphone transmitter under his shirt. (00:54:20)

Visible crew/equipment: When Skyler is rubbing oil on her stomach and preparing herself in the bathroom, a camera and cameraman's hand is visible for about a second from the left side of the mirror. (00:10:30)

Visible crew/equipment: When Walter walks towards Jesse's house when he hasn't shown up for work a camera and boom microphone shadow is shown on his back. (00:40:10)

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)

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.

4 Days Out - S2-E9
Visible crew/equipment: When Jesse declares he's going to start walking and sits up in the cot, Walt reaches out to him and a boom mic is visible at the top of the screen. (00:34:25)

Other mistake: In the famous mugshot of Walter against a height chart, the chart goes up in nice 2 inch increments until 5'8." It then jumps to 6'0", completely skipping 5'10". Did they forget there are 12 inches in a foot, not 10?
Suggested correction: This picture was never used in the show. This looks to be fan-made. Regardless, this picture was never seen in any episode of Breaking Bad, so it is not a valid mistake.
If the picture was used as a promo shot by the production team then it could be considered a mistake. If it's fan-made then the correction seems to be valid. Does anyone know the source of the image?
I can't find a source, but I don't recall ever seeing it in the show or in any ads, and in all honesty, it's pretty low-quality, so I seriously doubt it's a real production or promotional image. (The masking around his ears is quite bad, the "bruises" are digitally painted on - and poorly so at that, etc.) I would be willing to bet money on it being fan-made.
It's not in the episodes as the corrector says. But I never watched the show when it was 1st airing, so I'm unsure if it was used as a promotional shot and as such can't say if the correction is valid (though, as you say, the quality is low) so I would lean to the correction being valid.

Character mistake: When Walt steals the bottles of "hydrofluoric acid," they are misspelled on the labels as "hydroflouric." This misspelling is corrected when hydrofluoric acid reappears in season 4. This was corrected for some DVD releases but is still visible on some streaming services. (00:11:20)

...and the Bag's in the River - S1-E3
Continuity mistake: When Walt is sitting on the overpass it is clear that his car is parked on the part that straddles the median between the lanes, but when the shot is inside his car the view appears as if he is parked directly over the right lanes of traffic. (00:43:50)

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.

Visible crew/equipment: Just as Walt is saying the line about checking to see if the other one is dead in the RV, the edge of the set comes into view very briefly on the right hand side. (00:15:10)

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)

Continuity mistake: When Gus is showing Walt the lab, the washer leans forward with one item hanging out. Camera cuts and 2 items are hanging out. This is an instant cut and no time for the item to fall into the position. (00:21:20)

Continuity mistake: Combo takes the lid off one of the bottles of Cola. Camera cuts and it's back on. (00:27:00)

Cancer Man - S1-E4
Continuity mistake: When Hank writes Icebreaker on the board, the writing changes drastically. Note the A. (00:00:30)

...and the Bag's in the River - S1-E3
Character mistake: Hank finds the bag of meth in Krazy8's car. He picks it up to show Gomez and examine it. However, he does all of that in his ungloved hand. He then proceeds to place the meth in an evidence bag. (00:43:10)

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)

Continuity mistake: When Jesse is showing Brock his trick, he has his fingers pointed up in front of him. Camera cuts and now they are horizontal in front of him. (00:25:00)

One Minute - S3-E7
Continuity mistake: During Hank's interview, the tape recorder is constantly disappearing and reappearing on the table. (00:15:20)