That's what I don't understand... "the religion's view on X." What does that mean?
For starters, it means taking into account sources other than the Bible, which is not the
sole source of authoritative teaching - in Judaism there's the Talmud and related writings (redacted oral law), in Christianity there are the writings of the Church Fathers, etc. The bible text itself is not the only source.
Who is in charge of dictating what the religion's views are, when speaking on the institutional level? Isn't that what the Bible is for?
The bible is a good starting point, certainly, as far as Western religion is concerned, but as with any text open to interpretation, each religion has (or had, or tries to have) a central authoritative body. In Judaism that was the Sanhedrin, for example, and Roman Catholicism has the Pope.
Isn't it an infallable work of divinity? Supposedly?
That's kinda the basis for the belief system, yeah. But that doesn't mean it necessarily covers every possible nuance at a glance. That's where the authoritative body comes in.
The Bible is infallable, yet I have just shown where God not only accpets slavery, but tells you that you can beat your slave as long as they regain mobility (or is it consciousness?) after 2 days, because they are your property.
There are several approaches to the slavery issue that I've encountered. The first, most obvious one - typically associated with the fundie mindset - is the "How Dare You Be So Arrogant As To Assume Your Morality Is Better Than God's" approach. It has the "advantage" of not being refutable by logic, at least not to the True Believer.
A more nuanced approach views the slavery issue in its chronological context, i.e. as an improvement over a slave's position in other legal systems of the time. (There's also some confusion to the casual reader, in that there are two types of slaves: Hebrew and "Canaanite," i.e. not Hebrew, with different laws governing each type, but that's probably not for this thread). I can't really address that aspect, not being familiar with other systems.
Add to that the general trend of the oral law to moderate the seemingly strict statements of the written law, and to steward the system's evolution toward a "progressive" model. The evolution - as opposed to revolution - of the legal system is important in establishing a viable long-term approach. Change too much too quickly and everything falls apart. That's one possible explanation for the seeming harshness of the biblical commandments to modern sensibilities - although progressive for its time, it wasn't the end of the story, and the oral law kept the system developing (and in fact that's still the case).
With that in mind, the idea of capital punishment also takes on a new light. Although the bible prescribes four different court-administered death penalties, in practice the oral law interpreted biblical jurisprudence so strictly that the requirements for a capital conviction were rarely met; a court that executed anyone more than once every seven years was considered "bloody" (with another opinion in the Talmud citing a figure of seventy years). What appears in the text to be a harsh penal system took on a different character entirely through the oral law - one in which the biblically prescribed executions served more to illustrate the seriousness of the violations to which they were attached than to actually demand the death penalty right and left.
If a religious text provides justification, regardless of your stance, then who is to decide what the religion's view is? The religious people who disagree with you are going to do so with quotes that support their claims, while ignoring your quotes out of the very same religious texts.
Which is why (most?) religions authorize only qualified, recognized individuals to exercise authority. There
are certain absolutes on which everyone is supposed to agree. There are (or should be by now) established rules by which interpretation takes place.