Quote: lindsay janes

... I'm not sure what do you mean by "Lindsay's correction?"

The rest of that was "I wouldn't worry about giving a dog like Lindsay's corrections because in my opinion, he hasn't warranted it. What would you be correcting him for? "

and probably referred to this:

 Quote: lindsay janes

.. When he chose not to listen, what kind of correction should I give?

Lindsey, I agree with what Tabatha said. If he knows your cue, give it once and wait. If he doesn't offer the behavior, shake your head and wait some more. And slow down just a little bit with your cues...he is focusing on you in that video, but I'm not sure that he solidly knows what your cue means.

When he performs the command, click, reward and then get excited! Run a bit, pull out a toy, or whatever and incorporate more play into your sessions.

Don't correct him for not focusing, but like Cindy said, you want him to come to the realization that you are the source of his fun.

That may mean popping him back in the crate if he's being inattentive...

Lindsay,
At 2 years old your dog is probably fairly well socialized. This is merely an assumption on my part. Because there is another dog in the home I would not allow your dog to be around it at least till your dog is through the learning phase. At that point you might allow it at on a small increment of time and watch and see how your dog trains over the next few sessions. If your dog goes back to being distracted then cut out the socialization and go back to training and put him away so all socialization is being met through you.
Your video looks pretty good with a few exceptions that have already been mentioned. I can't tell if your using a word like good or yes (your choice) for a marker. If you don't understand marker training there is plenty of information on this site and others that will show you.
Be consistent with your body language, your words, and your tone or inflection. I personally don't talk much at all when training, especially in the learning phase. Don't worry about corrections until your dog is in that stage.

Thank you very much for training advice. They have been really helpful. I have started to crate Roo more often. I am working on re-establish the pack structure and hope it helps him with focus. I am taking a baby step and teach him what "sit" means once and wait for him to sit. If he doesn't understand, is it possible that I can show him what I want him to do then reward?

You can lure him into position and then reward, but I only give the command/hand signal once.

Edited because my advice didn't work in this situation.

Lindsay,
I like to start off with luring the dog into position also. If your using food just let him smell it or see it and then move it up just over his head and he'll rock back and sit down automatically, then use your marker (like yes). At that point I tell the dog "good sit". After the dog learns what I'm doing I will then use the word "sit" to get him to sit down then treat with a marker like "yes".
I also don't teach down in the same training session. Quite often what happens is the dog will begin to think the 2 behaviors are 1 and what you'll see is a dog that sits when you tell him to, then automatically lay down. You want to christalyze sit in that little mind.