Resource mobilization theory was a significant departure from previous theories of social movements, which were based primarily on psychological factors. Resource mobilization theory abstracts away from most psychological factors and instead treats human beings as rational agents, who act in their own self-interest according to the resources available to them. (In this respect resource mobilization theory was heavily influenced by rational choice theory in political science and neoclassical rational agents in economics.)
Under resource mobilization theory, people will not join a social movement simply because they believe it advances collective interests; they will only do so if the benefit exceeds the cost to them specifically. This is a somewhat cynical view of human behavior: Essentially, people don't join social movements to make the world a better place; they do it to make themselves better off---in some formulations, literally because they get paid a share of the bounty at the end.
I think resource mobilization theory is actually best at explaining failed social movements---they failed because they were unable to establish a collective identity, so they dissolved as soon as the individual cost exceeded the individual benefit. It is also fairly good at explaining the so-called "iron law of oligarchy" (which is hardly so strong as it sounds); when one oligarchy is overturned by a popular movement only to be replaced by an even more repressive oligarchy, this looks a lot like what resource mobilization theory would predict.
This kind of revolution has occurred many times around the world; most countries in Africa have undergone at least one. Idi Amin in Uganda, Robert Mugabe in Zimbabwe, Mobutu in Congo/Zaire, and Hastings Banda in Malawi are all examples of leaders who overthrew oppressive colonial regimes only to establish their own new brand of oppressive regime. They and their closest supporters benefited enormously, making their actions "rational" in the narrowly-defined sense of resource mobilization theory. Similar results occurred in the Soviet Union; while ostensibly the revolution was supposed to benefit the common people, mainly it benefited the leaders of the Communist Party.
Yet it's quite hard to see how resource mobilization theory can account for more successful and positive social movements.
The suffragettes in the US who fought so heavily for the right of women to vote couldn't have been acting in their own narrow self-interest; they were beaten and abused for months, all for what, the chance to fill out a ballot every few years? Their actions only make sense if they believed in something---if they thought of themselves as fighting not for themselves, but for all the women in America and perhaps even many women yet unborn.
Similarly, resource mobilization theory has no way to explain why so many White allies joined the Civil Rights Movement in the 1960s and marched with leaders like Rosa Parks and Martin Luther King; at least in the short run, it was hardly in the self-interest of White people to expand the rights of Black people. In fact, resource mobilization theory is even hard-pressed to explain the participation of so many Black people---because the costs of participation were immediate and personal while the benefits were delayed and widely shared. If resource mobilization theory were right, Martin Luther King would have had to essentially buy people off---pay them enormous wages to participate in the social movement, so it would be in their self-interest to bear the risk. That's a lot like what Robert Mugabe did, but it's nothing like what Martin Luther King did. MLK didn't pay people off; he persuaded them of the moral righteousness of the cause.
Some more positive changes may also be consistent with resource mobilization theory: The Magna Carta might be explicable in these terms, as the nobles who led the charge also benefited directly from the expansion of the rights of nobles, and there were few enough nobles that the benefits weren't too widely dispersed. Even the American Revolution makes some sense in these terms, as George Washington and Thomas Jefferson surely increased their own wealth and power as a result of the revolution. But even then, this explanation wears pretty thin; lower taxes were one goal of the revolution, but people rarely volunteer to fight and risk death simply to get slightly lower taxes. It was the representation part of "taxation without representation" that really seemed to matter to most people.
Resource mobilization theory may have been a necessary corrective to theories that assume that humans are perfectly altruistic and totally ideological, caring nothing for their own self-interest; but it clearly goes too far. Altruism and ideology clearly are major motivators for human behavior, as well as rational self-interest.