As I understand it, "perfect" in this context does not mean invincible.
Muhammed saw himself as very much human and therefore capable of erring/making mistakes.
I'm guessing you meant "infallible" but auto correct. Muhammed did say that he's a man as in he should not be worshipped, as Christians believe Christ to be God incarnate, but there are a significant number of Muslims including scholars who believe that Muhhamad was indeed infallible, in not just his message, which as a prophet he'd have to be, but also in all his deeds.
The Christian Bible also has quite a bit to say about slavery and its acceptable parameters.
It does acknowledge that it was an unfortunate reality of the world at that time, but in many cases it also referred to bond servants. Either way, God repeatedly tells the Hebrews to treat their slaves humanely and with kindness as "You yourselves were once slaves."
Fast forward to present day and arab muslims in Northern Sudan are enslaving black Christians from the south and the Darfur region with islam's sanction.
WWMD
What Would Muhammad Do?