This is going to be difficult to solve even with a solid definition of damage, because there are just so many variables involved. I really doubt you will be able to get a specific answer no matter how much detail you give. This is the kind of question NASA would solve with wind tunnel tests and weeks of supercomputer time. So consider my answer as a really rough guess.
If we're including hearing loss as damage, then your limit for observer safety is the speed of sound. Sonic booms will cause hearing loss, whether it's from a bullet, a jet fighter, or The Flash.
If we're not including hearing loss it gets a lot tougher. As things move through the air, they leave a pressure wave behind them. The faster you move, the higher pressure the wave. Also however, the larger your surface area, the higher the pressure. Last, the closer you pass by the sensor, the higher the pressure will be. Fighter jets will break windows if they go super sonic near them. So since your speedster is much smaller than a fighter jet, he can either go faster, or go the same speed but closer than the fighter jets. On the opposite end of the spectrum, bullets often are several times faster than fighter jets, and yet you won't even feel one pass by you by more than a few centimeters. Note in this video, he shoots through the gaps of a card house, and it barely budges. So a quick google search tells me that the speed of sound is 331m/s, which I'll take as the minimum for my jet fighter example. Another quick google search tells me the muzzle velocity of that 50 caliber rifle in the video is about 931m/s. Recall, my argument is that your speedster is smaller than a jet, and larger than a bullet, so he will have a pressure wave that's bigger than the bullet, and smaller than the jet. So this means your safe speed limit is somewhere between 331m/s and 931m/s.
This will vary with the weather by the way.