Continuity mistake: The kid who eats cookies sometimes keeps his hand closer to the biscuit packet, some other times closer to the computer. When Baby Yoda nags him for the first time cooing, you can notice his left hand on the desk under one angle and to his mouth munching in the other. (00:09:50)
Continuity mistake: When the Child steals the cookies with Force, the kid has his hands joined in a different way between shots. (00:10:25)
Continuity mistake: When the Mythrol says "Look, it's a mint Trexler Marauder", look at the stormtrooper closest to him. His hand is inches away from the blaster, but it's closer in the previous and following shot. (00:15:25)
Continuity mistake: When Cara Dune chokes out the Imperial comm officer, his cap falls down to his feet, but it's by his elbow as the shot changes. (00:16:05)
Continuity mistake: When Karga, Dune, Mythrol and Djarin are escaping, Djarin shields against a wall, gun raised up. From the opposite angle it's lowered. (00:18:36)
Visible crew/equipment: When one of the guards cries "Destroy it!" watch to the left of Karga and you'll see a crew member in jeans hiding behind a wall. This was later edited out on Disney+. (00:18:54)
Continuity mistake: Mando and the others just listened to Pershing's message to Moff Gideon. A band of stormtroopers is there to provide the patented generic shootout; notice Gina Carano shoot fiercely behind Mando right away, but in the next shot being idle with her arm lowered. (00:20:45)
Revealing mistake: After exterminating dozens of stormtroopers, our heroes are inexplicably pinned down by just two taking cover in the elevator. During this phase of the battle Gina Carano drives the big vehicle that was lying around and positions it behind the other two good guys (instead of in between them and the shooters). The two have to get inside the vehicle going through its narrow door; when Carl Weathers does it, it's of course not a surprise that the stormtroopers can't hit him, but it's a bit more surprising that in the view inside the vehicle he is still standing in front of an open door and not taking cover, but the troopers have stopped shooting. Someone forgot to add some blasters behind him, or the camera is really positioned at an unfortunate angle showing how exposed he is. (00:23:35)
Continuity mistake: Cara Dune drives the Marauder off the cliff; the vehicle practically nosedives and yet in the next shot it landed at a much less steep angle so it is driveable with no problems; in fact lands rear-first. (00:24:10)
Other mistake: The imperial base (that has been there for a long time) has troops on speeder bikes ready to launch, but no proper way for them to get out of the base itself, so a couple of them die just because the jump is too steep and they can't avoid the rocks! Imagine building a garage ramp 40 feet in the air and not even clear the ground underneath from huge sharp rocks. How would they even go back up? There's no towing equipment in sight. (00:24:45)
Other mistake: Cara Dune rams with the Marauder a trooper who was shooting at her through the open window. The speederbike explodes in a ball of flame, but despite the big open window that goes through the whole length of it, the flames do not affect the inside in the slightest. (00:25:50)
Continuity mistake: At the arrival of the TIE Fighters, Greef Karga spots them in the electronic sight of his cannon, but seconds later the turret has still to turn around from the time he shot the slow bombing trooper. (00:27:00)
Continuity mistake: When Baby Yoda barfs, he is holding the cookie in a different position between shots. (00:29:50)
Continuity mistake: When Captain Carson Teva tells Cara Dune "I am sorry for your loss" he turns towards a table. She is standing by a metal post, but she's leaning against it in the next shot, just as she was in an earlier part of the conversation. (00:32:25)
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.
