Let's say, for instance, I wanted to try the Cinnamon desktop in Ubuntu. Are there any dangers (in terms of stability & security) in adding the Linux Mint repository to my software sources? Should I opt instead for the ppa created especially for Ubuntu?
If at all possible you should use the PPA for Ubuntu. The ppa is going to be more compatible.
If you need you can try to use the Mint repositories, but mixing and matching repositories can be problematic. If you do so, use pinning and install the minimal number of packages from Mint.