Yes, it's his property, and he should be able to do as he pleases. However, two thoughts come to mind:
1) The pink fence. Sure, he should be able to paint the fence whatever color he wants for the side that faces his direction. But painting the side that faces his neighbors should have to be a neutral color -- you're not taking anything from him (it is a solid fence, so he'll never see the paint on that side, but the neighbors will).
2) The county should have notified the owners around the lake that this property was for sale. It would probably not have gone for $1,000. While the property owners should have gotten a survey before buying the property (I bought a house a few months ago and got a survey done to make sure that fences, garages, etc. were on the right side of the property line), if they had and found that the property between their house and the lake was undeveloped land, and it was not zoned for development, they may have accepted that. I don't dispute that this guy has a right to build a fence, but the county should have more public auctions, and at least notify others in the area. Sure, they published it in some sort of register, but no one reads those or should be expected to.
I'd bet serious money that a notice of the auction was printed in the local rag...
Unless Florida law is really strange, the county did publish notice of the sale, with a description of the property, in a general circulation newspaper. Or do you mean that the county should always provide direct, actual notice to owners of abutting properties whenever there is a tax sale?