I also find it hard to search for saved messages in Slack. If someone said something in Slack that actually needs to be remembered for more than a day, I'll just copy it into an e-mail so it can be searched for, archived, forwarded, etc. If the message would have been an e-mail to begin with, it would have been less work. If a Slack message requires more than a couple of sentences as a reply, I always reply that I'll be replying by e-mail.
So... not a big fan of Slack.
If you're in a thread and get tagged in another thread then you jump there. Now good luck finding the thread you were originally in. Tabbed threads would work a treat.
If each thread spawned a new tab, that would work. Main channels view, and each thread is just a tab. We live in a browser and an IDE, tabs are easy.