The health of your landscape is at risk. Car insurance is great but won't help much if they inadvertently drop a limb on your roof. If appropriate, ask to see current certificates of liability and workers' compensation. Take a look at their equipment. A dirty or wet climbing rope should flash a warning.
Safety is paramount.
The individual may be knowledgeable, but the crews may not have a clue of what is healthy for trees. Some arborists send employees to conferences. Some encourage employees to become certified as an arborist or tree worker. Ask about professional affiliations, licenses, and certifications. Training programs are available, such as the Electrical Hazard Awareness Program, hazard tree workshops, climbing, and pruning workshops.