The seat cushion on Martin's chair is placed sideways, with the stripes going from side to side. Most of the time the stripes go from front to back.
Daphne makes reference to a flashlight. In British English, a flashlight is called a torch. However, Daphne has lived in America for 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.
Roz's security camera is not set up well for monitoring a babysitter who may be stealing. However, if she moved the camera specifically to capture Frasier's overeating, the vantage point makes sense.
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.
While touring the TV station at which he hopes to work, Frasier asks, "Is there a sign-up list for the softball team? I'm sure that Frasier 'Slugger' Crane is going to be an asset to this station in more ways than one". Frasier would never say such a thing because as shown in "Frasier" (1993) {The Unnatural (#4.16)}, Frasier doesn't know how to play softball at all. The very title, "The Unnatural" is a statement on his softball ineptitude.