I am all for using existing resources to not only reduce cost but to reduce waste, but using
pallets in such a way is problematic.
The first problem you run into is getting the pallets there. You can get a few pallets for free here and there and even find lots filled with them for the taking on occasion, but how will you get them from point A to point B? For many of us that means making a trip with 1-8 of the things (depending on size of vehicle). Depending on how far you live from civilization (often where the warehouses and such are that have surplus pallets) this may or may not be the tipping point by itself but there are other problems. The
video shows a great design that will work very well, but to do so you have to use two pallets every 4 feet, to
fence in a 100x100 area (roughly a quarter acre) you will need then about 200 pallets.
The second problem is fastening them together. Will you use nails or screws? Even with the design shown you still need to fasten them together or the goats can "accidentally" knock one over. Figure a conservative estimate of thee nails per pair (which would be rather flimsy) for a total of 300 nails. Try driving a nail into a free pallet. Some are easy to work with others are so hard you need practice to drive a nail straight - especially doing it sideways. How many nails will you use and how much time will it take?
If somehow you get past the delivery of so many pallets to where you need them and have no issue with fastening together and can still save money they I congratulate you, it is truly an accomplishment and I always love to see resources used well. For a lot of people (like us) we would look towards other options for fencing first and save the pallets for small projects.