Yeah looks like something (a foam screen or similar item) is missing from that space. Not sure what that hole is for, maybe the cabin interior air intake. Example found online of what is supposed to look like:
Interesting. I'd say it's working as designed? We knew that the 2003-2004 has a slightly different setup than the 2005+. It seems that the flap door on the 2005+ opens with just the suction of the air? Does anyone know why the 2004 doesn't use any type of flapping door? Instead, it seems it simply gets air from the cabin when with the recirculation mode engaged, while the mechanism at the top opens up allowing cabin air to enter. If that's the case, why bother with the flapping door to also get air? Maybe because it's lower and gets more air from the footwell/cabin instead of from the top of the inside of the dash, making it more efficient?Two videos. Car is a 2005 Corolla LE.
First video shows just the fapper/door opening (and closing) when turning the fan on full (not set to AC/defrost). Air recirculation not engaged.
Second video shows what happens when fan on full (and then turned off) and the air recirculation button is engaged then disengaged. Not set to AC/defrost.
As both videos show the flapper/door on the front of the cabin air circulation housing opens and closes when the fan is engaged and is not dependent on; the air recirculation button setting or the air vent knob selector setting.