As for "what else":
Teach them that there's nothing shameful about carrying condoms. That carrying condoms doesn't mean they'll definitely be using them. And that you (Dad) won't assume that they're having sex just because they take condoms with them when they're out. Yes, this is my story - I was a fairly convinced Christian back then, and it was unthinkable (to me) that I'd have sex out of wedlock. Help your children out with plausible deniability if they need it: if you give them condoms, tell them it's okay to dispose of them if they aren't going to use them, that you aren't going to demand to know when and where and with whom (if anyone at all) they used them.
The mainstream narrative seems to be that teenagers are a bunch of gung-ho libidinous hormone bags with no concept of risk and consequences. But some are thoughtful, restrained and risk-averse - and it's alienating to them when you treat them as if they were the stereotype. The Condom Talk is one instance where this can happen.
Teach them how to find reliable information about condoms, and about sex in general, for themselves, and not from their peers (good for entertaining anecdotes, but not for facts). For themselves, because they might not be comfortable asking you. This might include knowing how to judge which websites give reliable info, or how to pick a random adult to ask (teacher: maybe good, doctor: good, taxi driver: bad). Kudos to you if your relationship with your kids is open enough that they feel comfortable getting their info from you, but prepare them also not to be dependent solely on you.
Live demo on an object seems like an obvious must-have, in hindsight. I know I'd have been mortified if my parents had given me such a demo, but I now also know it would have been the right thing to do. We didn't have sex ed in school back then, so that avenue wasn't available.
As others have mentioned, teach them about compatibility of materials. Show them a gross gooey old elastic band as an example of what happens to certain materials when exposed to some substances, light, or just time. Also that some people are allergic to this or to that, and that polyurethane condoms exist, too.
Heck, teach them about statistics, and that it's impossible to eliminate risk entirely from life. That condoms sometimes fail, and why they do, and whether and what second (or are these third?) lines of defence to use. That in some cases it's "game over" if the condom fails: as yet there's no cure for some number of STDs. That, despite all of this, humans take risks all the time, and are on the whole better off for it. And how to tell what risks are worth taking, and under what conditions one is more or less able to make such a choice rationally. Hint: while being drunk or sexually excited are not good conditions. Maybe you could even add in a bit of evolutionary biology: how the entire organism (including its mind) is built with one goal in mind1: making copies of genes. What a powerful adversary this is for a mere condom.
 Evolution has no "goal" and no "mind". Apply as-if rule here.