I used to “Pick up dead body.” as my friend’s wife said.
I did it a dozen or so times and every time, the person had pooed and peed. My friend who had been doing it for years said it was normal. The worse was when they were on their back and you turn them over. Wooooof…poo and pee beneath them.
As for an erection, never saw it, but it possible, or at least looks like it according to this article:
2. You (sort of) get an erection.
If you die face-down, your blood could also conceivably settle in your penis—which creates the appearance of a boner. But the chances of going out with a bang are pretty slim, says Judy Melinek, M.D., forensic pathologist and coauthor of Working Stiff: Two Years, 262 Bodies, and the Making of a Medical Examiner .
It’s actually more possible that your penis will look like it’s ejaculated after you’ve died. “Sometimes we’ll find discharge near the penis on a corpse, but this comes from the passive seeping of fluid from the prostate gland,” Dr. Melinek says. “It’s leakage—not ejaculate.”
https://www.menshealth.com/health/a19547721/body-effects-after-death/
Edit: This makes sense, since the blood is no longer circulating and will naturally flow downward. The first time I saw an embalming, I wondered why the mortician was massaging the person’s hand. He explained that he had to force the fluid into the extremities because there’s no circulation.
Can’t find it right now, but I’ve also read folktales of men ejaculating when they’re hung. By a rope around the neck BTW! 
I’ve also experienced the very first person I picked up, “snore” on the gurney. I looked at my friend who didn’t flinch and I didn’t say anything until we got in the van. He just laughed and said it was normal. I heard it a couple of times after, but never as loud.
5. You moan and groan.
When doctors try to resuscitate a person, they pump extra air into the patient’s lungs and stomach. But after you’ve died, that air can still escape—especially if someone applies pressure to your chest or stomach while moving your body, says Dr. Melinek.
And since that air is flowing past your vocal chords, it can cause a legit grunting sound. Which is obviously terrifying.
Weird Things That Happen to Your Body after Death | Men's Health](Weird Things That Happen to Your Body after Death | Men's Health)
The other thing that freaked me out on my first pickup is that most of the calls I went to with my friend were those on death watch, we usually arrived within hours of the death and usually the body temp shoots up like a fever. To get the sheet under them, you have to put your arms around the back or front and roll them to the side. Sure feels like they’re still alive!