I can't say I've enjoyed the shows much since Matt Smith joined, but I don't think that's down to him, but that the overall standard has declined from some well thought out ideas to "the half-baked jumble of silly notions" you refer to. But I don't think it is necessarily the case these need to be correct scientifically, since some of the most interesting stuff is of quite a different nature. For example, in one of the Christopher Ecclestone episodes a dalek gives a one liner to the doctor: "You would have made a good dalek". That's simply brilliant, in my book, since it opens a whole train of thought on exactly how they differ, and whether it is in fact true. And that, for the thoughtful kind of person, reflects into their own lives about whether they as different from some other group as they assume they are. To me, that is (science) fiction at its best.

I can think of perhaps a dozen such points throughout the series (hmmm, I wonder what the plural of series is?), but I can't think of any since Smith joined.