If you buy a Hebrew slave, six years he shall serve; and in the seventh he shall go free for nothing. (21:1-2)
It's interesting that the legal code begins with slavery. Obviously this was a touchy subject among the Israelites who were freed from slavery only weeks earlier, and perhaps they were uneasy and waiting to see exactly what form slavery would take under the newly issued legal code. As it turns out, the period of slavery is limited to six years, and the slave's family may not be disrupted. Both of these conditions, of course, are in contrast to the Egyptian slavery, which was apparently unending (Haggadah: "If God had not taken us out of Egypt, we'd still be slaves today") and involved babies being thrown into the Nile. Later on in Mishpatim, there are other laws relating to slavery. But perhaps these laws at the beginning are the ones the Israelites were especially anxious about and looking forward to.
If a man strikes his male or female slave with a rod, and he dies under his hand, he shall be avenged.
But if he survives a day or two, he shall not be avenged; for he is his money. (21:20-21)
It's hard to argue that if the slave survives for a couple days, then the owner is off the hook entirely. After all, seven verses later we read that a slave whose tooth is knocked out goes free. If the slave is killed, by the same logic the slave should AT THE VERY LEAST go free. And there's not even much satisfaction in the technicality that a dead slave cannot go free.
Notice that the passage twice uses an unusual word - "avenged". In ancient societies with weak central justice systems, the best way of deterring murder was to allow the victim's family to avenge the killing. The Torah preserved this system, though limiting it to the period before the killer could flee to a city of refuge or be put on trial. The presence of the word "avenged" here indicates that we are not talking about normal punishments, but solely about vengeance by the slave's family members.
It seem that if a slave were to be beaten to death, the slave's relatives could kill the master, just as in any normal case of manslaughter. This despite the master's excuse that he clearly did not intend to kill his own property. But if the slave survived a little while before dying, there would be an additional element of uncertainty. Perhaps the master's beating was not of a severity that could be expected to kill the slave, or perhaps the slave in fact died from some other cause. In this situation, because there are additional mitigating factors to the master's deed, the option of vengeance is not available.
In addition to the possibility of vengeance, it is not stated what judicial punishment you would incur by beating a slave to death. But the other laws in Mishpatim strongly hint that such a punishment did exist.
Eye for eye, tooth for tooth, hand for hand, foot for foot. (21:24)
The simple meaning of this verse seems to indicate corporal punishment, while modern-day halacha says that monetary compensation is required instead. These two interpretations must be reconciled with each other, as well as with our sense of morality.
At least one source in Chazal (Pesikta Zutrati-Lekach Tov on this verse) states that at one point in the past, corporal punishment was in fact practiced by Jews, according to the simple meaning of the verse. R' Yerucham Fishel Perle (in his commentary to R' Saadiah Gaon's List of Mitzvot, 3:29) has a brilliant interpretation of this which, in my mind, solves all problems. According to him, the basic law always required corporal punishment, but it was also acceptable to substitute ransom money for the corporal punishment. The Torah prohibits taking a ransom in place of the death penalty for murder (Bamidbar 35:31). But there is
UPDATE: the "literally corporal punishment" opinion also appears in the Gemara (Bava Kama 84a), where it is explained away as, basically, not literally meaning what it says. But in P.Z.L.T. there is no explaining away, and the logic behind the ruling is provided, so it is really really difficult to say it is not meant literally.
(Not my bekiut, but that of R' Amnon Bazak and the "Shabbaton" parsha sheet staff :-) )