When looking at a vine from the back, it is invisible, while when looking at a vine from the front, it looks fine.
Pretty much the same rendering as a ladder. Likely due to the new model system.
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Yeah, because it seems they forgot to add the "extra faces" like tall grass has.
It'd be cool if an option to disable backface culling per-face was added to the model format (creating a double-sided texture), as well as a "uv flipping" option, so when an non-culled backface was viewed from behind, the texture was horizontally flipped. This would allow image planes to be used without doubling them.

Well, there are 31 different models of vines, it would be normal to just want to finish it quickly.
Yeah, that raises another issue, the format should be more dynamic, like so we would only need to make 1 file for the model, the one where +Z is depth (currently the "model3.json" for models on the south-facing face, placed when looking north), we make the model and have a parmeter set like "autoOrient" so if a block rotated, it just did this automatically without inherited model files.
That'd most likely turn things with 4 rotations into 1 model file, and something like vines to be significantly less, too, as it would only need models for each of the non-rotated states of each combination and then those would automatically propagate how they should. This would, however not be default and resource pack makers could still do it the current way, but I think that 99% of resource pack makers will never make rotation-differing models. What use do I have to make a ladder facing east different than a ladder facing west? That's a niche idea in itself and I could only really see something like that utilized for puzzle maps.
Feel free to post any suggestions on the Minecraft Suggestions page on Reddit, such a redesign would fit there and not on a technical bug-fix list such as this.
fienxjox:
I'm not part of Reddit, nor would I consider joining for this. What I've said here are technical suggestions that most users on Reddit would likely downvote because "this doesn't affect me!", and anything related to resource packs seems to almost automatically get 20% downvotes. So something even more technical that most resource pack artists don't know about and have not used? Yeah, I don't see that going anywhere.
I'm not suggesting new mobs or blocks, just new options to an existing feature that would lessen stuff like this and make them easier to deal with. The only reason I'm discussing it here is because it actually relates to the issue. Much like if there is an AI issue one might suggest on how it could be fix or the issue lessened.
Also this occurs with ladders, but that doesn't matter, it's been like that since forever
PTR_91: It's also a different issue because ladders only are an issue if spawned in air or placed on a barrier, while vines grow downwards into air, and already appear like this naturally in swamps and jungles. Vines also had visible backs in the previous versions.

PTR_91:
Yeah, grum marked the bug on ladders backface being viewed on barriers as "Works as Intended" a.k.a, no backface will be added, as none is needed.
MC-46459
Here's an example: http://youtu.be/tElhuiJP8xw
(Video might not be viewable until 1:00 PM EST)
Yep, happening to me, too.