People hate being called liars. It's one of the most offensive things you can tell somebody (that is rated G). Similarly, telling somebody they are wrong can yield some nasty responses. Although the latter is less offensive than the former, it happens more often, which makes it a long-term aggravation.
If you think somebody is lying, ask them if the last thing they said was true. It still says that you don't believe them, but it is a far softer way of doing so. It is an implication instead of an accusation. If you think somebody is wrong in their claims or beliefs, tell them you disagree. That way, you simply have a different opinion.
There will be times when you need to be blunt. If somebody is being constantly shifty and you have proof that they are lying, then call them a liar. If somebody is making claims that are irrefutably wrong and are standing by them despite criticism, then call them wrong. Just understand that they are strong claims to make and can often make a situation worse.
If somebody has an opinion you don't like, they aren't wrong; you simply disagree with them. Never confuse the two.
Writing is a form of communication, as is speech. Both of them can be given to massive audiences at once or be one-on-one. I have always stressed the importance of being careful with your words, of knowing exactly what your words mean, both to yourself and to others, of making sure that you are expressing your thoughts as accurately as possible. Whatever your medium for communication, whatever the size of your audience, this will always be one of the most important points to know.