Thanks to the efforts of Erik Schilling, there are once again updated Tiled packages available for all recent versions of Ubuntu (or derivatives like Mint). Not only this, but the new official PPA also contains a
tiled-daily package that is updated whenever changes are pushed into the repository.
Actually daily builds for Windows have been available since a long time, thanks to Stefan Beller. I've now added a link to these to the sidebar as well.
If you want to see what's new in the daily builds, keep an eye on the commit log of the master branch, on which these builds are based.