Colchester: Currently building a new South American walk-through that will house silvery marmoset, Geoffroy's marmoset, golden lion tamarin, Linne's two-toed sloth and the long-tailed tamanduas. I understand some other collections (London) have similar setups.
Yeah, marmosets, tamarins and sloths are pretty much standard for a South American walkthrough exhibit with mammals.
Wow!

You'd think there would be a whole load of problems with an enclosure like that (e.g theft, the snakes biting people)
About them biting people; I actually don't think this is that big of problem. First off, most snakes (I guess also yellow anacondas) and animals in general only bite you if they feel threatened, like if you break their intimate sphere. And most average zoo-goers would rather pet a cute, fuzzy marmoset than these "nasty" and "slimy" snakes. I wouldn't wonder if far more people have been bited by marmosets and tamarins, simply because guests tend to break the intimate sphere of these species more.
About theft: Well, yeah, could be a problem. In Randers Regnskov Tropical Zoo in Denmark there is the snake walkthrough "Slangetemplet" (the snake temple). Besides all the snakes being harmless to humans, they are also relatively easy to get hold of again, should they be stolen (most rare species is probably the carpet python). Only problem is that when the rock pythons - which live in a separate exhibit in the temple - have youngs, they live freely in the temple when they are small. It's not allowed for private owners to keep rock pythons in Denmark, so it wouldn't be good if they were stolen.
Back to the topic, as far as I know yellow anacondas are pretty easy to get hold of again, aren't they? Even though safety measures should be taken, like having a keeper in the exhibit.