Throughout the scene where Martin (John Mahoney) brings out the new chair, and then Frasier (Kelsey Grammer) brings out Martin's old chair, Daphne's (Jane Leeves) legs keeps changing positions between shots. In some shots her legs are crossed, and in others, they are uncrossed.
Martin's (John Mahoney) chair appears to be in pieces even before it hits the sidewalk. Since the chair had to be dropped from a safe height, the chair was probably separated to ensure it would be wrecked when hitting the sidewalk. It could also be a result of it having to be reused in multiple takes.
Frasier has AZ bookends, but the Z is backwards.
Martin and Daphne are walking Eddie when the chair falls from above right in front of them onto the sidewalk. A minute later Martin is upstairs getting off the elevator to yell at Frasier for throwing his chair over the balcony. Frasier and Niles ask Martin where Daphne is, and he says she's down cleaning up the mess. Eddie is not with Martin. I don't think Daphne would be able to hold onto Eddie's leash while cleaning up the broken chair off the sidewalk.
After the chair falls off the balcony, Frasier and Niles meet Martin at the elevator. Frasier made a comment that an earthquake caused it to happen. After they go into the apartment, Martin yells at Frasier about setting the chair on fire and tossing it off the balcony, even though nobody had told him what happened, and the chair wasn't burning when it hit the ground.