As long as you are following FAA regs for drone use, and don't violate any temporary flight restrictions, such as fire or emergency closures of airspace, there aren't any issues with it over claims, BLM or USFS ground.

If you are using it for any kind of commercial purpose (including posting videos online) I think you need to register your drone and take an online drone test to get a license...

I do know that you can't pilot drones in national parks without specific special permits and exemptions...

Search on YouTube for "Drone Nightmare" and you should get something coming up about potential issues you will face. FAA can investigate you based on people reporting you
based on videos you have posted...

Generally, as long as you fly within the FAA’s rules and are respectful of people’s privacy, you should be fine. Check for local restrictions for Public lands but in general seems to be limited to National Parks, Monuments, some State or local areas may have their own restrictions, but really FAA controls airspace. BLM, Forest Lands usually ok unless temporary flight restrictions or nearby airports, FAA has an app to help you find those. I would be careful about posting drone footage without a commercial operators license.

I think they are an invaluable tools for prospecting. Helps you see stream flow before bushwacking in, helps determine the vegetation lines from past mining. Great tool.