Plot hole: The boss of the boss murders Werner Herzog because he knows that the baby is not in the crib. Yet it takes Mando's message (somehow intercepted) for the troopers to start moving in pursuit. The heck were they waiting for? They have overwhelming forces in the area and a previous deal with Karga. (00:33:10)
Continuity mistake: In the scene with all the Mandalorians just hanging out at some bar, Boba Fett retorts at Sasha Banks' character; "if it isn't the quacta calling the stifling slimy." There's a cut and his rangefinder is inexplicably tilted forward. It is back to normal in the rest of the scene. (00:06:15)
Visible crew/equipment: The kid actors in the school scene several times break fourth wall looking very distinctly at the camera. The kid directly behind the Child does it right away as Carl Weathers brings it there, and when Gina Carano is heading out there's a kid in the foreground who steals a worried peek at the camera, impossible not to notice. (00:09:05)
Continuity mistake: At the end, when The Mandalorian takes his helmet off so Grogu can see his face, the helmet is placed on the floor facing backwards. When Grogu is placed on the floor, it is now facing forward. Then when Luke walks away, the final shot shows it facing backwards again. (00:36:50)
Plot hole: Nick Nolte's little guy is supposedly terribly helpful towards Mando, showing him "the only way" to reach the enemy encampment, which is by riding the weird fishy beast, but when Mando surveys the target and the robot reveals itself, you can see that there are only shallow hills around the base, a large clear path of land, nobody even is on lookout...and most importantly, in the following episode, Mando makes it back on foot anyway, no blurrgs - and evidently the baddies had no vehicles, making them even less of a threat to begin with. And for being so helpful and good natured, he did not tell him to park the ship by/at his place nor warned him about the Jawas.
Revealing mistake: There's some sleight of hand involved when Cara gets her cup of tea from the repurposed IG-11. Maybe it was costly to have the animatronic arm working to the point of actually supporting the cup and hand it to her, so pay attention to what Cara actually does; Gina Carano is ALREADY holding the cup, taps the mechanical hand with it as if the fingers just released it from their grasp, and retrieves it. (00:11:50)
Plot hole: When the distress signal is launched, approximately 20 minutes are left till the arrival of the New Republic fleet. From the control room the team arrives to the prisoner's cell with 15 minutes to spare. They lock Mando up, and next time they communicate with their getaway robot dude, it says there are only 10 minutes to go, meaning it took them an astonishingly long time to navigate the ship without being really much closer to the exit, having met no opposition. Then the episode turns into a slasher movie of sorts, and somehow Mando manages to find them separately, hunt them down and as it turns out, not simply disposing of them, but also drag their unconscious carcasses to the empty cell he escaped from. There's nothing coherent about this timeline.
Other mistake: Somehow during the episode Cara and Fennec, on foot, manage to get to the base at the same time as Mando, who is on a truck. Moreover, Cara is the one with Mando's armor in a sack, but when Mando emerges from Slave-1, he changed clothes, and he's back in full uniform.
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.
Character mistake: Cobb Vanth says that he's never seen anything but the dragon's head and had no idea about the size of the dragon...but at the beginning of the episode we could see the beast pass through town (conveniently right in the main road without damaging anything else) and its enormous lengthy body was perfectly noticeable. (00:31:20)
Other mistake: The laser cannon punches decent sized holes into the columns and even cuts through the thick metal of the door (and look with what ease), but it is shown hitting the droid at least 4 times never managing to do any visible damage to it. When at the end of the battle they talk about the 'wound', it's not in one of those spots. (00:33:30)
Continuity mistake: In the opening recap of the episode a scene is shown where the Mandalorian is sending a speech to Moff Gideon, which was originally from the end of episode 15. In episode 15, he says "He (Grogu) means more to me than you will ever know," but in the recap he says "It means more to me than you will ever know."
Plot hole: Seeing The Child in episode 2-1 minute 10, Amy Sedaris' character shouts "Thank the Force." Up to that point nobody seemed to have the faintest idea of what sort of mysterious energy Grogu was using. It gets worse in episode 2-3 when Mando uses as greeting for the New Republic "May the Force be with you", which is used later other times. With the concept of Force being this ingrained in people's culture, it's inconceivable that *everyone* is completely clueless about Jedi, especially considering that Order 66 with the Jedi purge happens barely 30 years before the events of the Mandalorian, and several characters such as Kuiil or Greef Karga were alive and active during the time when Jedis were powerful and part of the administration.