Hey there.... I don't like analyzing swings because I'm a realist and understand that people swing differently. But, I'll give it a go. I'd also encourage you to read a comment I left for someone last week here:
https://www.reddit.com/r/golf/comments/3fosnh/best_videoresource_that_you_used_to_get_rid_of/ctqn1q0
Swing Analysis
You're swing comes outside in. A common mistake people make is thinking they can magically push that ball to the left and cure their slice - the opposite is true. You want to end up (normally) with a bit of an inside out swing. Once you've tamed your swing a bit, the link above includes a drill that may help you with this.
There's a ton of upper body movement going on here. On the backswing, watch your shirt buttons - they're heading toward the ground - you're bending forward. Maintain your upper body posture - think in terms of a body cast from the waist up if you need to. Think about where your swing path goes naturally when you bend down like that.... you naturally have to bring your arms across your chest to hit the ball - forcing an inside shot.
Your weight distribution and weight shift appears to be really, really messed up ;-) Video quality is poor, but it appears that you're ending your swing with the weight on the heel of your front foot. I think your rear foot is actually moving forward - and I don't think it's from hip rotation - it appears that you're literally "falling" through the swing - this is about posture and quieting your upper body and slowing your swing way down. Think about using the balls of your feet to distribute your weight - many of us put a slight (10-20%) bit more weight on our back foot to help initiate the weight transfer of a back swing. Try an effortless upper-body shot. It's amazing to watch kids swing the golf club - because they don't try to kill it they just nice easy swing.... that's what you want to do.... easy..... slow back..... and slow forward. You can adjust it later.
My advice is to start over on your driver swing. * Distribute weight evenly on balls of your feet, slightly more than shoulder width apart * Your ball alignment looks good here - just inside your front foot * Nice, easy, slow, effortless back swing with you left arm straight (looks like you're good on the straight left arm already) - keep your posture here, don't drop your chest toward the ground or let your right shoulder droop like you're coming inside. * Bring those hips around and let that right hand roll naturally over the left to close the face of the club at address. Let your weight shift naturally to the ball of your front foot and come up on your back toes without moving your back foot forward. * You sort of "fall through your swing" as if the follow through is just an inconsequential by product - end your swing in a good posture and freeze - is your belt buckle aimed at the pin? Is the weight on the ball of your front foot? Has your back foot scooted forward, or have you unnaturally squared your stance to the pin vs. bringing your hips through (this is why it looks like you're falling - like you have to square those hips or you're going to fall over) *Keep that head down - don't worry about the flight of the ball - let your right shoulder move your head through the swing - keep looking at the ground.
That wall of text is very likely what an instructor would help you with for a couple hours. If that's an option for you - it's a great idea. It takes a long time to cure a slice without really focusing on it. Most casual or beginning golfers make many / most of these same mistakes.
Good luck to you!!!