Oh gosh, there's been a lot of discussion again...
A few words on non-earth/non-present companions: I'll agree there would be (possible) problems I'd very much welcome it. Yeah, there are issues, like the morals.
I guess we have three possible scenarios:
1) Take a character who's not from present day London Earth and give him pretty much the same values and traits as present day humans. (That's a pretty generalizing statement but I think you know what I mean) This would... defeat the purpose of the character mostly except you might as well just use a normal human and don't need to spend a bunch of money and make-up and costumes and whatever.
2) Use a companion who for the most part agrees with present day values but has a few quirks. This would at least require some originality I guess since there are present day people who... well, have quirks and weird opinions on things. Like if we introduce a polysexual character (again), or someone who has very little moral qualms about violence, or someone who is used to being pampered, etc... Pretty much any character you can think of can be found somehow in present day society so is there really a merit to creating an alien or different-time human for it?
3) Have someone who grew up in a society entirely different from modern day Earth. That opens a whole lot of opportunities but it also raises questions, mostly how would that person fit with the Doctor's idea of what a companion should be like.

I'm not saying I'm against new, different companions, but I don't want them for the sake of being alien. I just don't want to feel either "why would s/he be a companion?" or "why did they go through the trouble of using an alien if they could have just used a normal person?" (Well, not from the "today is a tiny spec in space time" perspective but from the "what makes them more interesting than a normal person" perspective.)
There are possibilities for good-non human characters, obviously but they aren't blatantly obvious quirky characters.

Regarding references... I think it could even be funny if the Doctor tried to make modern day references at his alien companions only to realize they don't get them to the point of "I spent too much time with those 20/21th century humans" which could even be a serious plot point. (Possibly) (Then again, I think Who never was that big on modern day references... most blatant I can think of was Ten's Potter jokes)

And... while I think with Rory around for most of the last season I think I should correct my earlier statement a bit but I don't see the problem with having a slightly bigger cast again, like constantly a male and a female companion and possibly a third of either gender (or none, for all I care). But during the earlier seasons of the new series it really mostly was the Doctor and his girl companion and if the Clara era goes back to this it would be a bit disappointing.