Mediocre continues to have the definition you state, but the article is about how then being mediocre is "a bad thing, to be avoided" in itself. Yes, it's a bit 'meta'.
Being bad at ski jumping or being good at ski jumping is likely to get you recognised; being average is not.
A lot of their business and future articles are done by freelancers, and many of them are literally ripper from Quora (albeit with attribution).
Their news coverage is still good though, Lyse Doucet is a great journalist who did some fantastic coverage of the Arab Spring. They also manage to avoid shitting the bed whenever breaking news happens, as CNN in particular tends to do.
The rest of the BBC website, Radios 1 - 6 + Asian, TV stations (perhaps some of BBC 3/4 is bottom feeding), weather forecasts, world news, is awesome. That's just all I can think of off the top of my head.
Their articles are still decent enough that they'll make it to the front page of HN.
In specific areas they can be bettered, e.g. I prefer some specific football (soccer) websites, but this isn't a moan just a fact that they have to cover everything. As a general resource certainly for world news I think they're the standard to match.
I don't fully understand the reason for not using html5 video when on desktop, it functions perfectly.
I think their problem is that they've become a bit of a content factory, which links back to the whole freelancers thing. They churn out a lot of articles, and some are much better than others. It's the shotgun approach to getting views.
The "tyranny of excellence" undeservedly pushed "mediocre" meaning for many people down towards "bad", but "mediocre" isn't really bad; it's just barely average.