I use it to organize everything I'm doing. iTerm2 does splits, and both iTerm2 and Terminal do tabs, but using Tmux decouples my workflow from the operating system I'm using. Additional benefits are being able to close my terminal at the end of the day and reattach the next morning with all my programs open, being able to script things I do often, etc.
The screencast covers a lot of things, including workflow, key bindings, and tweaks to OS X to make you a faster developer. If you save ten minutes a day, you'll have made up the cost of the screencast in a day or two - which, in my opinion, is well worth it.
At the end of the day, it's whatever works best for you. I've been using tmux for a year and a half and it's just as important to my workflow as vim. I've had people complain to me that I'm too fast with vim + tmux (either people I'm pairing with, giving a workshop to, or just demoing some code). It works for me. Vim looks great for me. I'm able to think less about what program I'm working in and more about how I get things done faster and with less context-switching.
If you're using GVim or MacVim or some other GUI and it works, wonderful! If you're content with the speed that you're able to code, that's awesome. That said, back when I was using TextMate and Terminal, I thought I was really fast; and I'm probably 30-40% faster in vim than I ever was (or could be) in TextMate.
Clipboard usage is a bit odd; that said, how often do you spend using the clipboard every day? If the time spent mucking with clipboard is less than the time you save doing everything else... then you have your answer as to whether switching will be worth it to you. It absolutely, positively, with out a shred of doubt, is worth it to me.
Of course it's always whatever works best for you. But it's interesting to see what you win and what you lose before adopting cool things you hear from hero programmers in a podcast. ;-)
Although I don't see me using nothing more than a tmux session exclusively in the future, I already adopted some things for my server work and I'm looking forward to the pragprog tmux book.
