Continuity mistake: When "Blue" leaves the badge on the table, it at a distance of almost three times its width from the table border. When Cara looks at him going away, you can see the object being much closer to the edge. (00:32:35)
Continuity mistake: At the end of the episode, the officer opens a door to meet Moff Gideon. There's a lab technician kneeling in front of Giancarlo Esposito and another one standing while a third on the left is walking across, but in the next shot the leftmost one is already standing perfectly still. (00:33:45)
Other mistake: "Blue" checks out Cara Dune's record and talks to her in stellar terms, obviously she's a great gal. When Mando and her met in episode 1-4, Cara said that if she even tried to board a vessel registered with the New Republic, she'd be captured and be put in jail for life.
Plot hole: Mando's ship was completely wrecked, but two mechanics fixed it to top performance level and aesthetic pleasantness in a time shorter than it took for the Child to eat a small packet of macaroons.
Suggested correction: His ship was badly damaged, but mostly repaired by the Mon Calamari. The remaining repair work was less complex, but still took place over the course of several days. A space-faring civilisation being able to repair a damaged ship is not a plot hole.
His ship is literally falling apart (we see pieces falling off as it moves), the engines are barely functioning and looks like hell. It's not at all a mistake that a "space-faring civilization" is "able to repair a damaged ship", it is when the editing of an episode makes it look like two dudes fixed to pristine condition a wreckage in the same time it takes for a kid to munch his cookies.
Other mistake: In the first episode of the first season, the Stormtroopers in Nevarro were wearing poorly maintained and rusty uniforms, implying they were a small detachment stranded away and cut off from any remnants of the Empire, in fact living in a clandestine condition. They also had to set up a small laboratory in the bunker where the doctor worked. Now turns out that a few minutes off the city, there's a full base the locals were aware of, with tons of equipment, that is where the stormtroopers from Season 1 finale came from, and that the research facility is there.
Other mistake: Greef Karga mentions that the Mythrol was his accountant before running off, but when Mando captured him in the first episode, he had no idea who Mando was nor had ever seen his ship before.
Other mistake: In the first kill we see Ahsoka perform on-screen, the lightsabers don't cut anything, which is impressive since they leave scorching burn marks into a tree a moment later. (00:02:20)
Continuity mistake: The Magistrate beckons towards her to have a prisoner led to her. She is holding her spear with the left hand and gesturing with the right, but it's the opposite in the next shot. (00:04:20)
Continuity mistake: When Mando passes the gate to meet Morgan Elsbeth, the natural light changes in the space of a few steps. (00:11:30)
Continuity mistake: The Magistrate reacts to the Mandalorian's "My price is high" statement turning towards him. Both hands are on the bowl, while she had her right arm stretched out to feed whatever lives in the pond. (00:12:10)
Revealing mistake: Look at the droid carrying the spear the Magistrate offers to pay Mando with - it moves before she makes a motion for it. (00:12:40)
Continuity mistake: Ahsoka tosses to the floor the pauldron with Mando's signet. In close-up, it lands in a grassy spot between stones, but when it is shown again it lies in a different spot with no such big gap. (00:30:05)
Continuity mistake: During the clash between Ahsoka and the Magistrate, after they parried each other's blows and take a couple circling steps, the latter assumes a stance with the dull edge of the spear towards Ahsoka, but it's the pointed edge in the next shot (when she swirls it and attacks). (00:34:50)
Continuity mistake: After Ahsako has beaten Morgan, she holds her light saber up to Morgan's face so the tip is near the top of Morgan's head. In the next shot it's now closer to her neck and in the last shot, her light saber is almost parallel to the ground.
Chapter 14: The Tragedy - S2-E6
Audio problem: In the "Previously" section, Mando is shown telling Ashoka; "Bo-Katan sent me to talk to you." But the actual line in the previous episode was "Bo-Katan sent me. We need to talk." (00:00:20 - 00:16:20)
Chapter 14: The Tragedy - S2-E6
Continuity mistake: We can see Mando's position when he approaches the Jedi temple the first time, and the position of the shadows of the menhirs that form the stone circle. The camera view changes, and the shadows are in a different direction. (00:05:40)
Chapter 14: The Tragedy - S2-E6
Continuity mistake: When Boba Fett is talking to Mando and threatening him with Fennec's sniper skills, the weapons behind his back vary in distance from one shot to the next. (00:10:00)
Chapter 14: The Tragedy - S2-E6
Continuity mistake: When Fennec gets off the cliff to parlay with Mando and Boba, during the conversation the strap on her shoulder has a red clip on it or doesn't, randomly changing between shots. (00:11:20)
Chapter 14: The Tragedy - S2-E6
Revealing mistake: Once Fennec obliterates like bowling pins with a rock the ones she couldn't simply shoot, Boba Fett has another badass moment murdering the stormtrooper with the orange pauldron. Problem is, he's in the open and there's another stormtrooper directly behind him that couldn't possibly have missed Boba when he was busy poking comically the back of the officer but comes to life only when the camera is on him. (00:15:50)
Chapter 14: The Tragedy - S2-E6
Factual error: Boba Fett proves to Din that the armor belongs to him by showing him his chain code encoded into the armor. He then shows his father's chain code also encoded into it. Chain Codes are implemented by the new Empire in 19BBY. The second episode of "The Bad Batch" is about obtaining some of these new chain codes. Why does Jango Fett have a chain code when he died three years before they were a thing?