Hole in intake post air filter?
 

This is on my other car. Picture below for reference, the hole is between the flexible part above the positive battery terminal in the picture.

For now I just wrapped the intake with gaffer tape. Don't know how long it has been like that could be for about a year. It blends in there noticed it by chance today changing transmission fluid.

How bad could that be for the engine, sucking in dirty air and potentially water?

It's kind of dry rotted and wondering if I should replace it with an OEM piece or delete the whole airbox assembly and get an ebay "short ram" (hot air) intake.

http://image.superstreetonline.com/f...accord_k24.jpg

I would just go to an auto wrecker and see if you can find a car that has that OEM intake. Shouldn't cost more than 50 bucks.

Is this an Accord?

Don't you live around Brooklyn? Should be plenty of wreckers over in Larchmont that will have what you need.

Any type of open hole in your air filter is bad, the whole purpose of the air filter is to filter out contaminants, that hole is doing the exact opposite.