Slavery, homosexuality, and gender equality are three topics which come to mind, as they relate to the Bible.
In slavery, the primary 'moral inconsistencies and hypocrisies' pertain to elevating Jewish males above and beyond all other races, while also favoring males. If God's claim is being just, righteous, fair, and loving to all humans, then why favor only certain humans, for traits in which humans have NO authority to control (gender and race)? This appears inconsistent and more-so demonstrates human-only authorship of it's time, rather than universal objective laws and dictates. Why also consider such humans as property (especially if all humans are special - above and beyond all other creatures on earth)?
In homosexuality, it also again appears more-so written by only humans, who thought homosexuality was 'icky', like the majority of the population even thinks today, and yet, passed anti-gay law in the Bible as objective fact. It also appears fairly evidence the Bible was written at a time, before it was later concluded that whom one is attracted to is not a choice. Seems as though a universal and objective claimed God would not tell humans whom they are allowed to have life long relationships with, based purely on the fact they are the same gender. If they are two consenting adults, with the ability to make 'freewill' decisions, who is actually harmed in such a scenario? I also recognize, ahead of time, all the arguments one may present in opposition to this observation 
In gender inequality, the Bible stating women cannot lead also appears human inspired, without the aid of any divine authorship.
These are three topics which appear to warrant 'moral outrage', as to actually enforce such objective stated moral law would be only appealing to the subjective human opinions, written long ago.
As a Christian myself, I actually agree (with some admitted variance) that the use of oppression within society upon other individuals, as can be seen in most forms of forced servitude, or in some forms of sexual censorship, and in gender inequality, is cause for some expressions of "righteous indignation." However, cvanwey, as you know, you and I will probably still disagree over the nuances which we both think we see within the actual inherent makeup of these particular social and moral problems.
As for the issue of the Bible being inspired by God or not, that's not an issue I'm overly concerned with here even within this particular thread. Again, it's not an issue I'm going to argue people into or out of because I don't think it is a linchpin in our efforts to understand the Bible. It does contribute to our willingness to adopt what we read in the Bible, but our willingness is also contingent upon how we read it and what we think we understand about the meanings of the ideas we find within it's dusty old pages. Personally, I've always begun with the Bible at a grassroots epistemic level rather than at the traditional Top down, Hierarchical, Church Driven level; I don't believe the Bible is God's Word just because "the Church tells me so." Instead, I personally think one can just existentially read the Bible as an ordinary book and, as one moves through the hermeneutical circle to gain insight and understanding about its contents, the realization that there's something "special" embedded in the pages of the Bible can grow and emerge within the understanding of the person whose interests lie therein. The upshot of my existential approach is that I also have little to no expectation that I'll be able, or should be able, to CLEARLY AND DISCERNIBLY demonstrate to another person that the Bible is indeed some very special, sacred book above all other books. No, the imparting of that kind of demonstration will have to come from .... elsewhere, but not from me.
Anyway, in essence, I agree with you on some level that there is room for moral outrage when we see other people being oppressed. On the other hand, I think that we might also consider that our feelings of moral outrage are contingent upon what we each think qualify as bona-fide manifestations of immorality and injustice in our society, and in the three cases you've listed in your previous post, I'm absolutely sure that you and I have different perspectives on what we think we see is actually being said in the Bible about these three specific issues: slavery, homosexual discrimination, and gender inequality.
