Well, a non-interactive "temporal viewer" is logically consistent in that it introduces no traditional time travel paradoxes. That is, being able to view any information from an arbitrary prior date doesn't cause logical paradoxes (although it may conflict with thermodynamics and information theory somehow). However, actually traveling back in a way where one can interact with the past causes of course all of the illogic of time travel plot devices. David Deutsch in "The Fabric of Reality" actually explore the reality of building a real time machine by using the thought experiment of trying to build a virtual reality simulator/holodeck that simulates exactly the time traveling experience. If you allow past interaction and future recursion (e.g. you can change the past, which can change your own future timeline), you end up with a Halting Theorem violation, and a violation of the Church-Turing hypothesis, which may or may not rule out time travel devices, but at the very least, provides a conditional theory of time travel, conditional on the truth/falsity of the Church-Turing hypothesis.
Deutsch provides a "way out" explanation which will be somewhat unsatisfying for some fans of time travel. Time doesn't exist. Each instant of time is just another configuration of the multiverse. Time travel to the past, if possible, is actually travel to a parallel universe. Any changes you may there have no effect on the original "time line" that you came from. Therefore, there is no grandfather paradox. There's also probably no way to "get back" to the future/timeline you originally came from.
I prefer the illogical, but more twisted, single-universe paradox laden time travel plot devices. However, I like it when they use predestination paradoxes instead, so that the timeline can't be changed no matter how hard you try, and in reality, all your timetraveling was a closed loop that always was going to happen.
And of course, I love Hiro's character from Heroes.
He of course, recently discovered that he couldn't change the past (yet) as his travel became part of a predestination paradox (he ended up being the one giving MegaMemory Waitress her Japanese phrasebook birthday present, which means in the future, she had already met him, but perhaps can't remember much from six months ago due to her brain damage ala Memento. She can remember facts and figures, but can't remember personal experience from that time. Or perhaps she did recognize Hiro in the future, but pretended not to, knowing he would go back in time if she didn't say anything)