A New Yorker blog post (Screen Savers, posted by Macy Halford) has nicely surveyed the state-of-the-apps in the realm of religious practice.
In their sweep of the landscape they contacted Elie Kaunfer, who said some intelligent things:
...This is not to say that disputes about the value and use of digital texts do not arise. Rabbi Elie Kaunfer, the co-founder and executive director of Mechon Hadar, a traditional Jewish educational institute on the Upper West Side, said that arguments commonly arise in orthodox communities when congregants who are otherwise observant use their devices on the Sabbath. (There’s a term for this style of observance: “Keeping half-Shabbos.”) At Mechon Hadar’s yeshiva, where Kaunfer runs prayers three times a day during the week, he sees people use their devices to pray on: “It’s a little jarring,” he told me, “because you don’t know if they’re communing with God or checking e-mail.”Well said, and this latest revolution has just begun.
... many see seemingly negative effects of the digital era as evidence of spiritual vitality. Kaunfer, for instance, believes that the current revolution is not so very different from the one that occurred some seventeen hundred years ago, when the Mishnah (the Jewish code of law), hitherto communicated orally, was first written down. Then, he said, memory took a blow, and it has taken another one with the coming of the handheld device. But this isn’t necessarily bad: “In many ways, pulling text out of one’s pocket is truer to the way Jews experienced text in ancient times, when they pulled it out of their heads.”