1) Please remember that, when you are dealing with the public or the press in an official capacity (and to be fair, at all times with the press), you are expected to maintain and present a minimal professional standard in how you communicate and on the topics you discuss. This means that you will be held accountable for what you say, possibly in a way that is pretty harsh, so please do think before you speak. Ideally, prepare what you will say beforehand, and stick to that.
2) Do not make jokes. Humour has the property of falling flat or backfiring badly, and is very much tied to culture and social context. A joke that is funny between friends, because of a large amount of shared experience, might just be incomprehensible to others. In addition, jokes do need a good level of skill in delivery. You might have a Noble prize, and you might think that comedians are some sort of riff-raff, but comedians work pretty hard at creating jokes and at delivering them. Unless you have substantial experience in stand-up, chances are you are far less funny and witty than you think you are (please do show some of the intelligence you needed for your Nobel and ask someone who does not know you and need not respect you for your titles – you might discover you are less funny to a general audience than you are to your junior colleagues). Comedians can, and do, take risks with the jokes they tell, because it is part of their work. Given that you probably do not want to accidentally offend, or to be misunderstood in the 21st century, just stick to not making jokes.
3) If you are trying to be self-effacing, please be self-effacing. In case the term is not self-explanatory enough, you are meant to present your opinion as only one of the possible ones, your experience and opinion as the experience and opinion of one single person (as opposed to the truth), and so on and so forth. If you want to be self-effacing, you are using a rhetorical technique to present yourself as modest and humble to make your public feel sympathetic towards you (by artificially decreasing the perceived distance between them and you). It is perfectly fine if you use self-effacement as a ploy to come across as likeable. Please be aware that, if in your attempts to be self-effacing you denigrate or attack someone else (person or group), you are failing in your efforts, and do not be surprised if they get annoyed.
4) If you are dealing with a sensitive topic, please be aware of the difference in supporting your opinion with hard data and supporting your opinion with a couple of personal experiences or with hearsay from friends. It should not be that difficult to differentiate between the two.
5) Do feel free to share you opinion (in a professional manner, see point 1) about any topic you like. While you can share your opinion on whatever topic, be aware that people pay particular attention to the opinion of highly successful people (whether this is a reasonable thing to do or not is a different issue). Thus, if you say something controversial, there is a good chance it will cause a public controversy. If your opinion is not on a technical issue but on a social or political one, please go back and look at what I said at point (4). You might not think of yourself as a bigot, a racist or a misogynist, but your opinion might make you come across that way. If people do get offended by what you said, please take a moment to consider why people are reacting they way they are. Maybe what you said is something that a bigot, a racist or a misogynist would say. If you do not share those world-views then you might want to re-formulate your thoughts in a different way and apologise for your poor choice of words. If the matter is a 'misunderstanding', you should have prepared ahead to avoid such 'misunderstanding'.
I would also like to point out that, when controversies happen in public, a lot of anonymous people express strong opinions about freedom of speech and censorship online. Please be aware that the “internet lay person” interpretation of “freedom of speech” is often pretty far from the legal interpretation of the matter (which does differ in different countries and jurisdictions). Hence, do check beforehand that what you want to share will not land you in trouble, and be prepared if it does. In some cases you might want to kick a hornet’s nest. It does help though if you do it on purpose and not by mistake. As an adult and as a professional the excuse ‘I was just sharing my opinion’ just does not cut it, because here we are discussing the specific subset of human communication that falls in the realm of “public communication, on the record, in a professional capacity”. Most importantly, if you feel you have the right to say whatever you like at any time, that right then applies to other people too. These other people can then exercise their freedom of speech by criticising you, in terms that might feel pretty harsh (something that is ignored by the internet hordes on both side of the debate). Given these premises maybe it’s better if escalation is avoided.
I apologise if I sound prescriptive and a killjoy, but after achieving a Noble prize it seems quite silly if one were to make a huge fool of oneself for failing to understand and follow some simple social norms, and having some common sense. Please also note that, especially if talking to junior colleagues, people often get away with many infractions to the guidelines I give above. The obvious reasons for this slacking in the standards is because junior colleagues are, by the fact they are junior, less likely to speak up for fear of hurting their careers. Aside from the fact that taking liberties when in a position of power is tantamount to bullying, it also gives the false impression that nobody, ever, will call you up on what you say. That seems to be a very silly notion to entertain for someone who won a Nobel prize.