For all issues since February 2014 there is a new "viewer" frame which should enable viewing of the Vine on tablets and smartphones.
Clicking on the image of the cover will bring up a full-screen view,
At the top is a small control panel. On the left of this is a slider bar. Dragging it to the right will increase magnification.
There are left and right arrows to navigate through the pages, or you can use the side-bar on the edges of the page, or the thumbnail views at the foot of the screen.
You can also click-and-drag to pan the pages around.
To go back to the main website, click the X in the control panel or press Esc on your keyboard.
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For all issues up to and including January 2014, the "Flash Paper" format is still used.
Explanation of FlashPaper controls
Clicking on the hand icon gives you a hand cursor you can use to pan or drag the viewable document around
The I-bar icon can be used to select text, but as you can't do anything with it (like copy or cut) it's a bit redundant in this version
Likewise the Search box with the magnifying glass icon.
The slider icon enables you to zoom in and out of the page you're viewing
The wee boxes with little arrowheads give you full-frame or reduced-width views
The tiny box with a number tells you which page you're on.
The left-right arrows are for navigating between pages
The printer icon is self-explanatory
The final icon opens up another copy of the document in a new browser window, if you should wish.
There's an up-down scrollbar on the RH edge but no L-R scrollbar