I have a Macbook Air 10.9 and every time I launch Dolphin Emu, it opens like normal, then quits within 5-10 seconds, regardless of whether I opened a game or not. I have tried all official builds between 3.0 and 4.0, as well as Wintermute's builds, and still have the same problem. A little help?
Have you tried the latest build?
Get more details (like a backtrace) and create an issue about it.
Not completely sure what that is (noob here), but I looked at the log in Application Support/Dolphin and it had pretty much unrelated data.
OS X automatically dumps stacktraces (*.crash) in ~/Library/Logs/CrashReporter or DiagnosticReports. Pastebin 'em or put 'em in a Dropbox folder with the extension changed to .txt; I've done the latter since Dolphin just *loves* shitting out stacktraces for me.
Oh, this is actually something I run into regularly – do you have wxWidgets installed via MacPorts or Homebrew? Dolphin currently has a dumb issue where it'll pick up both its in-package wx libs and any you have installed via other methods, which end up conflicting even if they're identical. Try uninstalling any wx packages; alternatively, if you know how to compile Dolphin yourself, keep the system-wide packages and just rm -rf ./Binaries/Dolphin.app/Contents/MacOS/libwx* after building.
I don't have wxWidgets installed, and I don't know how to compile by myself. I'm not sure if I have any other wx libs, is there a certain directory to find them in and remove them safely?
Usually they'd be located somewhere in /usr/local (use Cmd-Shift-G to get there, or just Google around for how to make Finder show hidden files).