Email notifications - Some people really like to work from e-mail notifications. ASC has notifications for participation, following, points, etc. Just make sure they always default to "OFF".
Subscriptions - ASC already has this and is (in my opinion) the ideal way to find and respond to questions. Essentially, this is just searching on multiple tags. The subscriptions is an interface to let me define what tags I want to search for by default.
Sorting - Primarily, we need to see messages sorted by descending timestamp.
Sorting - I would like to be able to sort by both created or updated timestamps. Sometimes I want to see bona fide new messages.
Searching - This is ASC's big weak spot. Search is virtually useless on ASC. You have to really tweak the "filters" to get anything useful out of it. Re-do this and then back-port it to ASC please.
Threads - Thread view is all messed up. This thread (https://developer.apple.com/forums/thread/134075) is a good example. It seems to be organized hierarchically, with new replies to individual posts appearing immediately after the post being replied to. This is really confusing. Just order it by timestamp.
ASC has a feature to automatically guess the target forum (tag in these forums) from the content of the question being asked. That would be useful here. Otherwise, you risk everything going into "iOS".
Provide an easy way to see my own posts to see if anything has been updated. ASC doesn't really offer this. I have found a custom filter query that I use to simulate the "Inbox" of an old version of ASC. None of those custom filters seem to work over here. This is another opportunity to fix and then port back to ASC.
Filtering - ASC has a complicated system of filtering. Please don't import that.
Specialties - This is part of ASC gamification system. I don't necessarily mind them, but they aren't implemented very well on ASC. One has to perform specific actions, such as asking a question, to start earning a speciality. What about people who don't ask questions? How do you handle people with multiple specialties? ASC seems to pick one at random and display it, which is very annoying.
Guidelines - I think the Terms of Use need to be expanded and be crystal clear about what is allowed and not. I've just seen my first help wanted ad here. Is that allowed? I don't know.
Very nice use of Markdown in the editor. This is probably not something that could be ported back to ASC. Developers should be able to handle it though.
I like the documentation links at the top of tag results pages.