Unfortunately, I don't really have a lot to say about this article, other than that it appears to be a refinement of previous work by the author, i.e. http://arxiv.org/abs/gr-qc/0503077.

Specifically, I'm not quite sure how the proposal(s) get around the need for exotic matter for a compact time machine. Perhaps someone else will have a comment.

So this would have to be denser than a black hole?

Yeah, this is overly similar to something I seen on TV a while ago... The "we can only travel back the the point where we turned the machine on" was the give away...

Of course it's not possible to actually build such an infinite cylinder, so Tippler's time machine is only a mathematical curiosity, not a time machine in the sense of something that one could actual construct.

As far as Ori's time machine goes, in one of his earlier papers he has this to say about the compactness of his time machine:

I'm having a difficult time interpreting what this actually means.

Ronald Mallett's time machine http://en.wikipedia.org/wiki/Ronald_Mallett perhaps? That one has been discussed here previously. My personal opinion is that Mallett has not satisfactorily addresed how he purports to have gotten around Hawking's proof that a compact time machine must violate the WEC. Ori states that his time machine is in some sense not compact, but I don't really follow what Ori is saying here.

I'm not sure if there is any way to directly demonstrate that the universe is not compact, but since we can show the converse (in at least some cases) the question is addressable by science to some extent.

Part of the issue is related to the fact that we can only observe part of the universe, the so-called "observable universe", so we can't necessarily directly test all the topological properties of the universe as a whole.