Image Source: ClipArt
Permits and Clearances

If you start shooting video on open space, a park ranger may require that you have a permit. Whenever you know you're going to be working with a production crew on government land or private property, you first need to gain permission to access areas that are otherwise off-limits or restricted. 

Other places that are off limits to productions unless you get permission first: shopping malls, supermarkets, clinics, recreation centres, public schools.

Sporting events and political conferences may require certain press credentials. Find out out what if any requirements there are and how they apply to your production before you send a crew on location. Better safe than sorry, and you'll be protected from any legal action if a production assistant slips on a cable or gets arrested for trespassing.
Copyrights and Releases

Don't assume you can use other people's work in your production. All work is copyrighted unless you acquire it from Public Domain or Creative Commons, or unless you get permission from the source. Anything you can get from the Web is subject to copyright. Don't expect that you can Google an image or download a pop tune and then use it in your production. Fair Use might apply in some educational projects, but that doesn't mean you get to decide that it's fair use if you intend to broadcast your work (uploading and playing your video on sites like YouTube would be considered a broadcast).

For documentary work, it's often necessary to use Release Forms that the artist (or interview) talent will sign to give you permission to use their likeness or work in your production. When doing news you rarely need to use release forms when interviewing people, but you will still need credentials and even permits depending on the location or event. And you still need permission to use copyrighted work, which also includes photos from social media sites.

Basically -- Always respect others' work.