That last part caught my eye, and so I did some digging and I found the catalog of incoming channels. I've compiled that information below along with the relevant links to make it easy to browse. The archives for each show include very high quality videos and any closed captions or subtitles that could be captured. These are captions are made searchable for easy research. Once you find the program you're interested in, you can stream it on the website and watch it as much as you'd like - but unlike most items on the Internet Archive, there is no download button. "Loans", however, are available.
These "loans" are a bit curious. The Internet Archive allows users to "borrow this program from the Internet Archive library on a DVD-ROM for 30 days for a processing fee. Internet Archive does not sell or license this content, and all loans must be returned within 30 days. Please note that this is a copyrighted work and performance, copying, or sale, whether or not for profit, by the recipient is not authorized. Loan fees include shipping. Expediting fee is required for each expedited program. Multiple programs may be sent together or separately. If dissatisfied for any reason, the fee is refundable if the DVD-ROM is returned within 10 days." The processing fee is $25 within the U.S., $45 for an expedited loan and $75 for an expedited loan outside of the U.S. The loan fees seem fixed regardless of the length of the program or the quality of the video.
In addition to the download button missing, these TV news items are incompatible with the Internet Archive's zip_dir.php process for serving up compressed zip files of items. Does this mean that users are stuck paying the processing fees if they want offline access? Not at all. Once you find an item you want to save a copy of, say BBC America's BBC World News aired on March 10, 2015 9:00 - 10:01am EDT. The URL should look like:
https://archive.org/details/BBCAMERICA_20150310_130000_BBC_World_News?q=news#start/19/end/79
Now that take URL and replace "details" with "serve" and you'll get a list of URLs for each file in the item. It should look something like: 
In that example, the captions/subtitles are located in .srt, .txt, and .idx files while the video is available in .mp4 and .mpg files. Users interested in listening to the news as a podcast on their way to work can do so by downloading the .mp3 file. Simply click and select 'Save As' to locally archive a copy of one of the files.
Channels captured* by Archive.org as of 9/11/2015**:
Channels previously or intermittently captured:
Special: NSA clips, searchable by speaker, quote, keyword, time and channel. Curated by Robin Chin. This is a great resource for journalists, historians, activists and curious citizens.
Not every channel that's being recorded has a public collection. Find a link that I missed for one of the channels? Find a channel that I missed due to intermittent (but regular) recording? Let me know and I'll add it.
*This does not include manually added items recorded from TV broadcasts.
**See here for older programs and channels no longer being captured, and the various sub-collections, or use the advanced search feature on this page.