Kenny gives Frasier a poster that he tore off the side of a bus. When Frasier unrolls it, you can clearly see that it's just plain, black paper.
Daphne makes reference to a flashlight. In British English, a flashlight is called a torch. However, Daphne has lived in America for almost several years by this point and had previously talked about improving her English, so obviously she would learn to adapt to using the American version of certain words.
When Frasier is helping the boy hit the pinata, they are holding onto a long pole. After Frasier hits the pinata a few times, his phone rings, and suddenly the pole is a small stick. This is because the pole actually breaks as Frasier is hitting the pinata. The broken end is clearly visible while he's talking on the phone.
Around the 3-minute mark (when Martin is showing Frasier a new trick he has done with Eddie) the hand of the dog trainer can clearly be seen on the right hand side of the screen.
As Frasier is walking towards his room (right before Niles says "Frasier, you're not famous anymore."), in the top left corner, you can see a boom mic enter the frame.