Oh boy this thread is a gem! I work on a small breeding farm and I've seen some.... pretty awkward things. We one time had a stud who was getting on in years and it took him a while to climb up on a mare and do his job. To make matters worse on this particular mare we were running out of time and had this one opportunity to breed her or lose our stud fee (which we were in desperate need of for various reasons). Well he climbed up and stood there for about ten minuets and nothing happened. So my boss helped him down and went to collect his semen. Well about halfway through collecting the geezers semen he parked out and knocked the cup out of our hands and onto the muddy ground. Of course my boss shouts: "Grab it!!" and we're scrambling in semen and mud to collect anything we can. Of course he was just eating off to the side and here we are covered in unmentionable grime and trying to decide if we should even mention to our vet the lengths we went to get the sperm. Our vet couldn't stop laughing when we told her and handed her what we got. (Good news is we got paid!!!!)
Other than that I don't know if this would count as gross or not but I was on foal watch and the mare was having a pretty rough time. The colt was huge and I do mean huge and so we were doing as we had been taught as we waited for the vet to arrive and trying to coax him out. When our vet arrived she thought that the colt would be dead from asphyxiation and told us to just pull as hard as we could to try and save the mare. Well, guess who got regulated to that job; yup: moi.
So like any dutiful prevet/apprentice I start pulling on his legs and trying to ignore the fact that I was probably pulling out a dead baby and fighting against the contractions. Well the mare decided to take mercy on me and heaved out a massive contraction. Unfortunately it was at the same time as I was pulling back and I ended up pulling the entire foal (about 100lbs of foal actually) and stumbling backwards and hitting the wall with the baby (covered in muck and..... oh gosh) squishing me. Then to make matters worse the baby started to move and thrash and push all the grime that he was covered in into my mouth and ears. Of course like a dumb*** I didn't let go of him so we spent about five minuets wiggling around in his mothers gunk and getting madder than heck at one another.
The (same vet as above) was my savior as she pulled him off of me and when I looked down I realized that somehow in our struggles (probably from him being like a donkey and sitting his butt onto my hands at various points) he'd gotten his first rectal exam and I had officially done my first exam.
We both ended up fine and are no longer that mad at each other. (Though not sure we'll still be amicable in May because I'm the one who has to pin him down when he gets gelded! )
These are the only two 'majorly what the heck' moments I think we've had so far (after about forty years of doing this).