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Copyright and Trademark Issues
For both screencast and live video capture, you must be careful not to use images or other content that is copyrighted unless the content license specifically says you can.
Before you object, let me bust some myths:
Fallacy: because we are using these in a lecture (educational) setting, we're protected by fair use. Fact: while there are definitely Fair Use exceptions that apply, they are narrower than most people believe. This excellent Wikipedia article
summarizes it pretty well, including the fact that fair use as it applies to trademarks is different
from fair use as it applies to copyrighted works.
Fallacy: because we're not making money from the use of the content, we're protected by fair use. Fact: Copyright restrictions are orthogonal to whether you're making money from the content. Fair use considers many factors, of which this is just one.
Fallacy: if it's on the Web (ie found by Google Images), I can use it. Fact: putting something on the public internet doesn't weaken its copyright protection in any way.
Content that is probably OK:
Content on Wikipedia and in the Wikimedia Commons can generally be used as long as you attribute where you got it from. Read the license on the page containing the content to be sure.
Microsoft Office comes with a clip art library whose license expressly allows reuse.
Content you've redrawn or created yourself is of course OK.
Clip art or stock images or clips purchased from commercial sites setup for this purpose are OK, since such sites usually exist expressly to allow you to pay for content which you can then reuse.
To learn more, or consult with an expert regarding a particular scenario, start with these important guidelines and further help available from UC Berkeley Libraries.