I wouldn't want to see a derivation of the circles theme, seeing as they've been with us now for nearly ten years. If the BBC were in a position to rebrand their channels, they should be making them feel as fresh as possible.
You are correct in not using lettering in your logos.
The ones you've got to change are One, Two, Four, Sport (that's the worst one), and Parliament.
BBC News is OK if you put news underneath it, otherwise it looks like BBC World.
Not too bad for a first attempt. We've seen worst......
For Parliament, perhaps you could use the BBC election logo? In the U.S. CBS News' politics account on twitter uses their election logo as more of a CBS Politics logo.
When you look at what we might call 'iconic' logos, very few of them actually state what the service/app/company does. Using your logic: Twitter = Bird, Facebook = f, Spotify = Green circle, Nike = Tick. The BBC One logo doesn't have to state 'BBC One', because it would become well known as it is used more.
All the logo's you mentioned there, aren't exactly comparable. The Nike tick is unique to Nike, while the generic free clip art gears you've used, are pretty much everywhere.
The impression I get from this mock is that you've spent only a small amount of time on the logos themselves, and spent far too much time on the PDF, and (again) animation.
The only symbols that really work for me are the ones that aren't original. The BBC cloud symbol (or close derivative), the children's channels' logos, even the BBC Three logo - they all stand out as far better than the non-symmetric cube, the ripples, and the "camera focusing" symbol.
Some of the decisions in the style guide are bizarre. The safe area doesn't appear to be the EBU standard, which might not matter so much were it not for the permanent BBC DOG tightly squeezed into the corner.
I don't see the sense in having the BBC logo on its own permanently on each BBC channel in a position that will be awkward on many TVs.
The credit squeeze makes the credits far too small for no particular reason; the font choice for the credits makes them look incredibly cheap, especially considering the size of the text. Surely you'd end up with credit sequences that are far too long in order to fit all the credits in.
Century Gothic as a font choice in general seems a poor one. Obviously, a mocker doesn't usually have the luxury of a custom font for their mock, but it seems like this one was chosen simply because it was in your list of typefaces. As a font, it lacks a variety of weights; to me, it just looks like a cheap version of Futura (especially the way it is executed here).
The actual execution of the symbols is especially poor. The BBC Two symbol in particular looks sloppy, with the aliased edges on the diagonals, the lack of symmetry where it appears there should be, and the one pixel "steps" in the vertical lines that have been overlooked.
The BBC One symbol also looks like a poorer execution of what we have now, as the curves wouldn't form a circle if the two ends were joined. Just tweaking the shape to achieve that makes the execution a lot better, if not the idea.
The design of the style guide itself looks like a PowerPoint exported as a PDF (and I suspect it is). The text dominates the page, and for me it gives too little breathing space, as it were. However, the design of documents would be a large section in a style guide by itself, so it's probably not worth putting too much focus on it.
Overall, I can appreciate time has been spent on the mock. However, I'm unsure as to whether it's been spent in the right places.
The new BBC Three and CBBC logos, whilst abstract, still represent the name of the channel. I think that's what's missing here, particularly with BBC One & Two. The obvious fix for Two is to just use the '2', BBC One is a lot more difficult though.
2 - The execution of the logos is poor. For instance the actual BBC Three logo is slightly darker than your backing for it so you can see where the original has been cropped.
The mismatch between the backdrop of each logo and the backdrop to the elements is evident on every logo bar the BBC Four one when I printed the page of the style guide out with the logos. Well, it was the second time - the page size of 26.67" x 15" meant that I only got a small portion of the page when I printed the first time.