COPYRIGHT
Probably an area of major oversight, especially by short filmmakers.
The law regarding copyright is fairly simple: If you've created it then you own it. However, what you create must not contain creative content that has been produced by someone else who retains copyright. However, this must be in the context of originality.
Basic Example
If you go outside and film a bird flying in the sky, that piece of footage belongs to you, and nobody else can use it without your permission. If you add a soundtrack created by someone else then you must assure you have permission from the soundtrack artist before using it, and, in most cases, you will have to pay them a small royalty fee.
You can film anywhere within the public domain without obtaining copyright permissions; however, if there is music being played and it is picked up in your recording then may be required obtain permission to use that music. Permission must be sought when filming on Private Land, National Trust areas, land owned by the Ministry of Defense and similar type areas.
A Common Mistake
Many people believe that if you are not making a profit from your video then you don't have to seek copyright permission. This is not true. You can be prosecuted regardless and whether or not you are making a profit. Profit only determines how much you are fined.
There are various different types of copyright such as Performing Artists Copyright which is when you are recording a live band and Master Recording Copyright which is when you want to dub in a particular piece of material (such as a CD) which source must not be altered or re-performed.