Potential fix for BT Broadband connection errors (Cabbage, Currant, Centipede)
This may be entirely a coincidence, but since I've not read anything about Bungie fixing the issue themselves, this may be worth a go for any PC players getting the aforementioned error codes, especially if using BT as an internet provider.
I've been reading a lot about the way BT handles DNS, and that it's not very reliable when it comes to IPv6 adresses. I used the site http://test-ipv6.com/ to determine my IPv6 connectivity and it scored 9/10, failing the "Test if your ISP's DNS server uses IPv6" part.
According to a couple of online articles I read, there hasn't been any way to change the DNS settings in the router since the Home Hub 1, but you can alter the settings manually from the adapter properties in control panel on Windows. Changing the IPv4 DNS from auto to manual and selecting 126.96.36.199 and 188.8.131.52, and the IPv6 DNS to 2001:4860:4860::8888 and 2001:4860:4860::8844 has allowed the IPv6 test to score a full 10/10 through my browser.
Initially I got a lot of connection errors stating the Destiny servers were down, but after a few attempts I was able to complete missions without the game kicking me out each time, so unless Bungie has actually implemented a fix in the last few hours, it seems the IPv6 issue is what's causing all these disconnections