A big issue seems to be that, owing to the nature of the kinds of questions that get asked on EL&U, questions that may be interpreted as 'unprofessional' or 'embarrassing' may appear as 'hot questions' on the StackExchange multicollider (dropdown in the top-left corner of the screen), as well as http://stackexchange.com/. Would it simply be a good idea to limit 'hot questions' that may appear in the multicollider to sites which are likely to have subject material that looks 'professional'? I suspect this would involve preventing EL&U questions from appearing in this list. Would the community have a problem with this? Is it a good idea?
The mods have previously agreed that whenever a question is dealing with an "offensive" term, we protect it as soon as we see it. Pre-emptively.
So, one idea we just had in chat would be to take protected questions off the Collider (and the cross-site ads, and the Twitter feed). Wholesale. After all, "protected", by definition, basically means just that: we don't want newbies or outsiders to be participating in it.
The problem is that newbies or outsiders are defined as people with less than 10 rep, while the newbies coming via the MultiCollider typically have 101 rep via the 100-point account-association bonus. So we need a way to deal with that effectively.
(Simply increasing the threshold from 10 to 102 won't cut it, because we don't want to be shunning 101-rep users completely. They can still provide awesome answers, and often do. We just need a way to stop advertising certain questions across the network. Let people find those questions by themselves, if they are really interested.)
I suggest (and strongly support) a way for the site moderators to mark1 questions so that they do not appear on the multicollider (and twitter, and sidebar ads on our sister sites, etc.).
It's not that they are not fit for the multicollider (and other such advertising), but that they tend to bring some type of traffic that we don't want to handle on specific questions: the questions in themselves are good and well, and can be discussed in a suitably academic fashion, but they conjunction with a lot of incoming traffic is bad. Moreover, they give new users a biased idea of what our site is about (we’re not Urban Dictionary).
I think the proposed suggestion goes a long way into helping fix both. This community would do better by having a steady, organic growth than forced waves of new users from heavily-advertized teenager-appealing sex-related (or, in some case, extreme-geek-appealing!) questions.
 in any way deemed technically fit, it's a policy decision, the implementation details are something else
 yes, EL&U is successful: this use of the expression “organic growth” is one idiom that I learnt here, on EL&U, when I was just a newbie. I have learnt a lot from being in this community.
I have three unrelated answers:
the multicollider exacerbates the 'rich get richer' problem of those questions having high local voting then getting more to pile on from 'outsiders' (people join up just to vote a popular question even moreso).
I particularly like the 'democratic' aspect of this site, that things that are popular get voted up, and that things that are unwanted get voted to close. In fact I particularly dislike it when closing occurs autocratically by a single mod (however well-respected and high-rep they may be, and also however much I agree with the closure).
the multicollider is great because there is no easy way for me to see questions on all the sites I like without intentionally visiting each one separately. The collider does a little bit of that for me. And I tend to like those sites that have high popularity items on the collider.
Would it simply be a good idea to limit 'hot questions' that may appear in the multicollider to sites which are likely to have subject material that looks 'professional'?
I think you are missing the point. As much as I also hate the multi-collider, the issue is that these sorts of questions are mostly likely ungood wherever they end up. Getting sucked into the multi-collider just makes it more obvious. But if there is a question on our site we would be ashamed of having on the multi-collider we should get it off of our site. As in, remove our crap; not hide it from others.
If I got it right, it seems you're suggesting this SE doesn't treat about professional stuff, but even if there are some questions that really are not expert or professional, I've seen very good questions on here.
The solution is not for us to "back off" from the multicollider, but rather to work so as to make our StackExchange more professional.