What are Green Addresses? Is it true that they can solve the "confirmation delay" problem, and how does that work? Are there any drawbacks?
The green address is a third party trust trick and can help resolve most problems related to the need to wait for confirmations (slow transactions).
To make it very simple :
Service A publishes its green address, service B decides to trust service A.
When someone send bitcoins from service A to service B, he will send from the service A green address.
The service B knows he can trust the service A, he knows A won't double spend, so B can credit the sent bitcoins immediately, without waiting for confirmations ( or waiting for just one confirmation, which is probably wiser ).
This is mostly useful for transferring bitcoins b2b (business to business), typically it would help making arbitrage easier and faster between 2 bitcoin exchanges, if both decide to trust each other's green address.
This can also be useful to allow for POS (Point of sales) with instant transactions if the POS can trust the green address of your bitcoin bank (or online wallet)
As an individual, I could also negotiate with my local supermarket to trust my green address (providing them my IRL address, ID number and more if needed). Once they decide to trust my green address, I can pay immediately with bitcoins at my local supermarket (they trust me and won't need to wait for confirmations).
The green address is just a bitcoin address, but it's a "from" address people decide to trust and accept transactions from this address without waiting for confirmations.
Possible drawbacks are :
Less anonymity, or even no anonimity at all ( always using the same public from address), which is not a problem for a business, and its even great for public accounting/auditing ( yes bitcoin can also help fiughting corruption ! )
Blockchain spam (more transactions for the bitcoin network), which is a good thing if the blockchain can scale.
Encourages people to use trusted wallet providers (some kind of bitcoin banks). Here too, this have good and bad sides.
It's not enough to create a green address, you still need to be trusted so that your green address is useful
For now, afaik, only mtgox.com, btcpak.com and instawallet.org support the idea. To be useful, green address system needs to be widely adopted by bitcoin pools, exchanges, online wallets, businesses, etc.
As a few have suggested, Green Addresses '1.0' had issues.
Some improvements that were suggested as early as in 2011 which you can see implemented in GreenAddress prevents users from double spending transactions via multisignature thus allowing zero confirmation for third parties that trust the GreenAddress provider, yet preventing users from risking their funds in someone else's online wallet.