Unlike other systems, where the "developer makes available, people use" deployment strategy is used (Windows, I'm looking at you), with UNIX-like distros, there's usually a package manager and some team managing its packages.
The main point is so that everything works well together. At least when I used Windows, the usual thing was that a program would update DLLs if it had newer versions to install, but nothing ever controlled whether everything would work well with the new version of the library, you're just adding more files to the jungle, if anything breaks, it can break badly.
With package management, new versions are (or should be) tested before being made available, so that you don't have downstream issues. The problem you may have with non-distro packages is that they may have not been really tested for your distro, or may lack dependencies or restrictions in the metadata. This is about packages. If you are going to install from a developer instead of waiting for your distro to release their package, go for packages. As far as you stay with the package manager, you don't risk making a mess out of your system.
If you decide to compile from sources or simply unpack a tarball, think twice before doing a make install to the /: you may overwrite files or add files which the package manager is not tracking, and this may break your system, by installing incompatible files, by changing settings in a way you can't undo by removing the package using a package manager, etc.. This is also the reason why you never want to use developer-provided install scripts (nVidia drivers...).
Think of this like entropy: package managers do actually keep track of it, so it can violate the second law of thermodynamics if need be. When you use a third-party install script or just make install, you're increasing the entropy of your system without keeping track of it. Once you've done that, your only chance to make sure you remove anything you added is to restore a backup or to reinstall the system.
TL;DR:
You're bypassing distribution-level testing, which tries to catch issues specific to the software distributed in the same distribution.
You're bypassing the package manager, possibly leading your system to an unrecoverable state, if anything goes wrong.
In the end, like @jordanm said, weight the pros and cons. If possible, look for third-party packages for your package manager that, at least, will help you with the second bullet above.
