Does anyone have a link to a video of a dog with a paddling gait?

No video but I'm sure I could get one next time I go to a dog show ;)

No video but look at Rachael Paige Elliott's Dog Steps. She has drawings that will show you just as well.

I'm looking for something on-line, I don't want to pay $30.

Sometimes an education costs $$ (and it's $$ well spent!).

Rachael Page Elliott's book is a classic. Well worth the $30.....if that's all it is. There are drawings of every movement problem you can think of and t iwill be useful well into the future. If you really don't want to pay money for a lesson well learned, go to a dog show and sit ring side. You'll pick up on paddling quickly by the end of the day.

I would suggest go to a major entry show and sit ringside. Meet up with other breeders be quick to listen to what other more expereienced breeders say. You will learn a lot about gait and you will see some paddling along with other flaws. There will be movement you like and don't like. Not all good movement is rewarded. Labradors should have smooth,effortless movement. They should move with purpose. The best learning tool is actually getting out there and seeing the variety available (type, movement, etc.) so that you can decide what you like and what you think is correct.

For those who might be interested, the book mentioned in this thread "Dog Steps", is available from Amazon.
Paperback for $17.99

Not a video, but are good descriptions of WHY a dog 'paddles' -

Too long in pastern or too great an angle in relation to the foreleg, will result in loss of spring, over extension of the ligaments and a looseness (paddling effect) when viewed from front-on during movement.

http://www.weim.net/emberweims/ComeGo.html

That link is very good. I would have added "lifting" which may be related to "paddling". What I mean by lifting, and others may not use this to mean the same thing, is when the rear out drives the reach of the front so instead of the shoulder opening resulting in the forward reach, the dog lifts at the elbow and raises the front foot to give it more time in the air as it drives with the rear. This is often caused by a straight shoulder or a short upper arm, or just imbalance front to rear. I think I have heard the term "hackney" to refer to a more pronounced form of lifting. And again, it seems to me that lifting is related to paddling.

The thing is, people post pictures of their dogs in motion with the intent of showing reach. But, the front foot should be close to the ground and not raised in the air. Reach is determined by where that front foot touches the ground and how efficiently it gets to that point.

I would love more experienced people than myself to comment.