As I see it, there are 2 differences:
1. Without the final 了, the sentence doesn't sound like the speaker has finished speaking. They'll probably go on saying something else. With the final 了, the speaker can actually stop there.
2. With the final 了, it means that the action (of watching TV) has been going on, and will probably continue if it's not interrupted. Without the final 了, the sentence can be interpreted in more than one way, depending on what is coming after the sentence.
Both correct. Can I write the last 了？ - Yes Does that change the meaning? - that depends. For example: You worry about your kid or are so surprised to know that he's been watching TV for 3 hours, you might add the last "了". What if you remove the last "了" in such situations? Luckily, they are STILL correct. So, the last word "了" is kind of a word that helps you express the emotion you have. But not tipically be used in written Chinese, by the way. (though commonly seen in elementary schoolers' compositions) Hope helps.