To them, a drone is a drone regardless of whether it's being used by some moron thrill seeker or by your company to inspect a radio tower or a bridge. This means that it's important to make sure that your company, and anyone your company contracts with, operates professionally and responsibly.
So here's what you have to do. First, make sure that any drone you're going to use for your business is properly registered with the FAA, that it has the required markings, that you've made sure that the missions you have planned are allowed by the FAA, and that you have applied for and received any waivers you require for your flights. Then, assuming your planned use of a drone passes muster, do some thinking before you start flying.
It's important that you think about how you plan to carry out your drone mission with an eye toward safety and with consideration of the impact of the drone might have on those who observe it. For example, if you plan to inspect an antenna on top of an apartment building, perhaps it's a good idea to alert the occupants of your plans so they won't start calling the police when they see a drone outside their windows.
In addition, if you're considering the use of a drone to cover an event that is likely to attract the public (which is probably why you're doing it), then planning the flight so that the drone won't pose a danger to spectators or event participants really is a must.
Even if the flight over an audience is allowed by the FAA (which it usually isn't), the last thing you want is for it to fall on top of someone.
In addition, you need to make sure that the drone pilot can see the device during the entire mission. It's not enough to depend on the video feed from the device for your operations to be safe.
The only way to avoid incidents is to be able to see around the entire drone, which is something the on-board camera can't do. Also, keeping the device in sight during the flight is the only good way to ensure that you don't lose the data link that's controlling the drone.
Finally, if something does happen to your drone, then make sure you own up to it. It's bad enough to be identified as the company that crashed its drone on national television, but it's worse if you then appear to be covering it up.
By all measures, 2016 will be the year of the drone, but it's up to you to determine whether that's a good thing or a bad thing.