When the staff prisoners show Hogan where the tunnel in hut number 3 is, it is under a small sink in the middle of the hut, but when the prisoners are entering the tunnel to escape, it is against a wall. Then, when Klink arrives after Newkirk tells him it is in hut number 3, it is in the middle of the hut again.
After LeBeau gives himself up, the guards are distracted by the other two prisoners in the tunnel, and LeBeau runs a short distance away up a path (to pull the dogs away and cause additional distraction). Klink gets in his sidecar and leaves his quarters/office. LeBeau, now being held at gunpoint on the path, distracts that guard by trying to sell him the two dogs that followed him (LeBeau). After the guard takes the dogs' leashes away from LeBeau, there is a cut, and Klink and his motorcycle come right through the same path where LeBeau was being held at gunpoint - only now LeBeau is in the background, standing with Newkirk and Carter. The distinctive rock formation is visible in the background in both shots, showing that it is indeed the same pathway.
When LeBeau opens the outside trapdoor at the end of the tunnel, it opens upwards. Second time he opens it, it slides across. Update: This is not necessarily a goof. The cover is obviously not attached in any way - it just sits in a groove around the exit. It makes sense that LeBeau would tip the tunnel cover up to scout out the area, since just dropping the cover down if necessary is easier and more likely to set in the groove properly than sliding it off and back on.
Sargeant Braden explains to LeBeau that Private Mills and himself had to dig thru 400 feet of rock and dirt when they escaped from Stalag 9 yet their clothes are clean and have no mud or dirt on them.
When Braden drops down into the water truck's tank to escape, the sound of his boots hitting the bottom of the tank is quite obvious. Therefore, there is no water in the truck's water tank.
A distraction is created by having Newkirk pretend he is sleepwalking so LeBeau can escape from the camp under the fence wires. Yet, when he comes across the mass of escaped prisoners from Stalag 9 they use the tunnel to get them all into Stalag 13. Why didn't LeBeau use the tunnel to begin with and avoid having to use a distraction.
As Braden and Mills climb up the ladder and onto the water truck, the sound of their boots banging on the truck and the water tank is loud enough that the guard standing beside the truck's cab would have heard them, caught them, and discovered everything - before Hogan could set things up to distract the guards.
After Newkirk, LeBeau, and Carter give themselves up, Klink arrives in the sidecar of his motorcycle. He asks one of the guards if he got them all, to which the guard responds affirmatively. Klink would have immediately ordered one or more guards to search the tunnel, both to see where it originated and to catch anyone hiding in it, even though the guard had just assured Klink that all the prisoners had been caught.