Water in cauldrons and Blocks with a translucent texture (flowing and still water , ice, Nether portal, End portal, Maps) inside an item frame appear correctly translucent as long as the HUD is activated, but turn fully opaque when the HUD is deactivated via F1. Attached are two screenshots of the same scenery, one with HUD and one without.
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I see what Tails sees: usually translucent, opaque dependent on the angle. In 13w06a. It doesn't seem to depend on graphics settings. Also they change to opaque when in the game menu (ESC), and when in any kind of inventory.
Still in 1.5.1, attached debug crash incase it's graphics card related.

Fixed for me in 1.7.2 (except Cauldron water, but that is never transparent).
Indeed, fixed in 1.7.4
This even happens without turning off the HUD in certain angles, confirmed.