The Captain's suit is completely dry in the next shot after he gets soaked with soapy water.
When Moe asks Curly what the problem is, Larry can be seen getting out of the car twice.
The soap in Moe's hair disappears when they rush out of the shower after hearing the bell.
When Curly falls down the fire pole, they use a stunt double. Curly's double lands on top of Moe and the double's hat falls off, but when Curly takes back over his place in the next shot, his hat is still on, then it falls off again.
When the guys are in the shower and seen only from the shoulders up, they realize the fire bell is ringing and come out of the showers wearing rain coats that are covering their shoulders.
When Moe is helping Minnie out of the car trunk, she accidentally kicks the actress behind her in the jaw. Looking closely at that actress's face, she can be seen to hold back a grin.
The same people who are walking past the car that the Stooges and the girls get into are shown in the background after the Stooges crash the car, even though the locations are far apart from each other.
Notably Eddie Laughton and Moe and Curly's real life Father Solomon Horowitz.
When Moe pushes the big lamppost off of their wrecked car, it falls directly in front of the car. However when the car drives off on it's own, the lamppost is now out of the way.
At the very end of the scene where Moe and Larry are smacking Curly on the rear-end with the hoses, you can hear the director, Del Lord, yell "Cut!" right before the fade-out.
When Curly says "The birthday cake!", his lips don't move.
Larry tells Moe to take a shortcut if they want to beat the Captain to the fire, however they never heard the actual address of the fire so how do they know where to go ?
A boom mike is visible in the picture window on the street just as Curly is about to fall on the cake.