My main annoyance with tmux is the inconsistency of clipboard integration support. There are terminal-specific hacks* that mostly resolve the problem, but those become ineffective when I have to work on another machine (where I likely don't control what software is installed).
* For urxvt users, add the following to your .tmux.conf:
set-option -ga terminal-override ',rxvt-uni*:XT:Ms=\E]52;%p1%s;%p2%s\007'
