You're misrepresenting Khan I think. Labour has its antisemites, god knows, but Khan's been vocally critical of Corbyn and his failure to handle this and I can't find any evidence or reason to suggest he holds such views. To quote him on it:
I am an advocate of the Labour leadership, including the NEC, actually receiving some training on this stuff as clearly they don’t understand what racism is, and there is no hierarchy when it comes to racism. There are too many examples in our party of people having these views, and action does not appear to have been taken quickly enough
Source:
http://www.theguardian.com/politics/2016/apr/30/sadiq-khan-antisemitism-row-damages-labour-poll-hopesEven if you look at Goldsmith's literature the attacks are literally all cases of "Khan was at the same event as this guy", "Some guy who was in the same office thought this" and "When Khan was a defence lawyer he acted on behalf of this guy" none of which
in any way actually mean that Khan holds the same views as those people. And whilst I'm sure you'll be sceptical of me saying that, it's definitely not just me, or just people on the left, who think so. Former Tory chairman said it was an "appalling dog whistle" campaign and the leader of the Tory group on the London Assembly has been heavily sceptical as well.
(
http://www.independent.co.uk/news/uk/politics/sadiq-khan-wins-london-mayor-election-result-2016-zac-goldsmith-a7017106.html)
You're welcome to dislike Khan for other reasons, but frankly the evidence that he's an anti-Semite (unless you have some stuff I don't know about/isn't included in the recent media stories) is from what I can see about as well put together as the available evidence that I'm a Tory.
Anyhow more widely: first thing to bear in mind is that low seat swing like this is really unusual. It's normal for parties to gain or lose triple figures of seats. As such I think "no confidence" is too strong. Labour held all but one council across England, it's not a vote of no confidence and it's not a collapse but it's a definite vote of "meh" for Corbyn. He's certainly not inspired any gains (except maybe in hoovering up a few Green seats in places like Norwich). The media also basically let Corbyn's enemies pre-set the standard he was being held to and then knife him for not getting there; from an independent analysis losing seats and a council is disappointing, and Scotland was total murder, but the "we should be gaining hundreds of council seats" thing that some of Labour's right were trying to spin was really not that realistic given that their 2012 results in these seats were already very strong. I think you're right that he's not done that well, I just think that it felt like the press were hawking in on the "Corbyn referendum" narrative rather than actually paying much attention to what was going on in individual areas.
I also agree that the Tories haven't done at all badly, this is a very solid result, though the few southern English councils we had were pretty rotten for them - they made OK advances in northern areas against Labour, but they have some cause for concern in the south where they lost out to Lib Dems and UKIP quite heavily. I was mostly annoyed at the coverage there where they put out early stories saying "Tory council gains" and then had the pundits repeating that long after it became clear that they were actually going to take overall losses. Which is just bad/slow reporting tbh.
UKIP did a bit better than expected in Wales, I do think that they needed to make bigger gains in England. Since their surge (2013) this is the last set of council seats that haven't been elected (these were last up in 2012). As such they were starting from a very low base, and in 2013, 2014 and 2015 they gained at least +100 seats each year. That growth seems to have slowed down a lot this time, +20 or +30 is obviously a lot lower. They're doing well on a few individual councils (Dudley and Thurrock were both good news for them), and I suspect they'll sort of solidify in some local areas now, but they didn't get many gains in a lot of the "old Labour" northern territory where they wanted them. Next year will be UKIP's really big test though - without an EU referendum coming up, and with a lot of seats to defend, it'll be their first really big test for holding ground. This year's not a disaster for them by any means, but with a weak Labour party and a load of free coverage this seems like a real missed opportunity from their POV to get big gains in the north of England.
Also finally on UKIP in Wales, it looks like Neil Hamilton may be going to
challenge Nathan Gill for the Welsh leadership, which might rip their Welsh party apart rather. Whatever one's views on UKIP as a whole, Hamilton is a horrendous candidate, lost his Tory MP's seat under a cloud of corruption allegations in 1997 and now he seems to be trying to get up to the highest office he can grab in UKIP.