LOL-The mouth is going to be the most risky of these choices (followed closely by the nose). You want to be very careful when handling bird poop/cleaning cages etc. You can get quite sick, even if you and your bird are healthy. I am not saying you
will , but you
can. If a healthy bird pooped into the mouth of a healthy person (
directly, as in 100% poo into wide-open mouth-lol/ew) that would be a fairly high-risk situation. I might call the doctor and I would monitor symptoms closely. I would even consider running a gram-stain or testing on my bird's poop (just in case I eventually contracted something and needed to know what it was)...The risks would increase if the person or the bird were sick.
E coli, for instance is a common oral-fecal risk (among myriad others). Eyes and nose could also be pretty bad in theory, as inhaling poop particles can lead to fungal infections of the lungs (among other things)...you could get pink-eye (conjunctivitis) from poop in the eye etc....If your bird has any transmittable illness (psittacosis etc) you can get those by ingesting poop particles.
Fecal matter of any sort is full of "crap" (tee hee hee) that you do not want to enter your body. Some of the things in bird poop that don't hurt them much can be harmful to us. That having been said, they can also get sick from eating their own poop!
IN TERMS OF THE EAR LOL---It is a good question!
Aside from something minor like an ear-ache, I don't think you would get very sick from it (if at all) unless you had a SERIOUSLY low immune system (Assuming your bird isn't carrying parrot fever or bird-flu lol) and assuming your ears are intact structurally (no punctured ear-drums etc).
It is a valid question though because the alternate route of entry(ear) could pose unique bacterial/fungal hazards in relation to the sinuses/brain etc....but for the most part, only if the structure of the inner/middle ear was damaged in some way.
Honestly, if you have ever swam in lakes or ponds, I imagine you have had various forms of diluted fecal matter in your ears already lol. In my non-professional estimate, the biggest concern following a poop to the ear would be a blockage/secondary-infection from the introduction of foreign matter+bacteria (depending on how far back in your ear canal the poop was able to travel lol). Maybe an ear-infection or fungal issues (especially if the blockage wasn't cleared).
I would probably flush out (+drain and dry) my ears ----I would flush with a diluted peroxide mixture (after very thoroughly wiping off any external debris). I wouldn't stick any q-tips in either...
I don't imagine a possible position in which you would ever get a direct poop bullet to the ear lol...in any given scenario, most of it would external.
However, from a purely analytical ( slightly off-topic) perspective, there are instances in which the MODE of introduction (of pathogens) significantly impacts the overall systemic consequences of the pathogen on the person (as demonstrated by
Naegleria fowleria, a brain-eating amoeba that has been found in bodies of water in the USA, as well as properly processed/municipal DRINKING-water
). Now, I mention this,
not because you could ever contract "Naegleria fowleri from your bird's poop, but because it has to enter a Peron's body in a very specific way in order to do harm. When ingested, it has no ill-effect; it only poses a hazard when introduced into the sinuses through the nose! SIDE NOTE: That is why Neti-pots (sp?) should always be used with distilled water.
https://www.webmd.com/brain/brain-eating-amoeba#1
I wonder if there are any amoebas/bacteria/viruses etc (non-bird related or bird-related----just in general) that have to enter through the ear....
Again, I am 99.999999% positive that you will not find any of these things in your bird's poop. I have officially veered off topic.