I find mutual altruism in my self-interest: we scratch each other's backs. If I get pleasure out helping someone else, that is fine ,but the point is to help the other person for her sake .Government is society's way of our being mutually altruistic in social services.

Any other Randian logical flaws?
Mutual altruism is something of an oxymoron. Enlightened self-interest can mandate that one assist another person for a number of reasons, in exchange for a future return, as an investment in a person who may make a valuable contribution to one's own benefit, or to encourage an environment where one may receive such assistance at a future time if needed. Some examples may be a business donating to a school, which would help ensure a supply of well-educated potential employees, or to boost a local market (by increasing potential income for the region through education and training), or to increase the businesses good PR and therefore brand marketability, or simply to receive a signifcant tax write-off. This is apparently altruistic on it's surface, but at base it is actually enlightened self-interest motivating the action.
There is no such thing as government altruism. This is one of those areas where Rand's idiosyncratic language causes problems. Altruism is the voluntary rendering of material or non-material assistance to another without expectation of profit or reciprocation. When you include government force in that, it ceases to be voluntary, and therefore truly altruistic. It is the use of threat of violence to compel others to contribute to a collectivist conception of support and assistance. It is motivated in most cases by what appears to be enlightened self-interest; but is at base simply fear or laziness. Fear that one will not have a "safety net" should one fail to adequately support one's self, or laziness in not wanting to work too hard to support one's self when on can rely on someone else's support and assistance.
The problem with Rand's exposition of her theories is that she used one word, altruism, for two completely different circumstances. One, that of forced, collectivist contribution to a supposedly universal safety-net support system; with the tacit assumption that those receiving said support had a right to it simply for the fact of their existence, and their demands by nature took precedence over the desires of those who actually produced the means of support. This is primarily what Rand was fulminating against.
However, she also uses the term to refer to a different sort of altruism, that which is truly voluntary and free; but which was motivated, not by any sense of fellow-feeling, but by the same priority of demand by the supported/consumer over the desire of the supporter/consumer, which resulted in an abnegation of self. This is, I think, where she went wrong, since she mistakenly equates the two, when they are clearly two completely different phenomena. She also denies the existence of true altruism, or even the appearence of such as enlightened self-interest; instead believing that all altruism was false, and either of the first kind or the second.
This latter is also where her primary objection to, and rejection of, relgion originates; seeing it as simply another form of forced collectivism, using emotional blackmail instead of outright force, to achieve it's goal.
But in both cases, it's the putting the value and primacy of the group over that of the individual, and the non-productive consumer over the producer, that forms the basis of her objections to both.
The biggest objection that I can see is not her opposition to government-mandated charity, which I tend to agree with; but her denial of the validity of private and personal charity as well. It is in the case of those who are disabled and unable to achieve full self-sufficiency where the flaw in her philosophy shows itself most prominently. She draws no line between those who are still able to produce and contribute to their own support, albeit in a limited manner, but instead choose not to, and demand that others bear the entire burden of their support; and those who are disabled and unable to support themselves to any substantial degree, and would not survive without outside assistance.