I have a 1.5 hp table saw motor rated at 115v/16amp. My garage has all 20 amp breakers but all outlets are 15 amp. Does the 15 amp outlet present a hazard if the wiring and circuit are all rated at 20 amps?
Just change out the receptacle
I bet your tablesaw has a 5-20 plug on it, which won't fit into a 5-15 receptacle. Since you have a 20A circuit, though, there's nothing wrong with having a 5-20T duplex receptacle on it, or even changing all the receptacles on the circuit to 5-20Ts from 5-15s. This shouldn't be too tricky a job, as long as you turn off the breaker before you start (of course), change the receptacles one at a time, and note down how things were wired before you start unhooking them. Also, if the existing receptacle is a 15A GFCI, it'll need to be replaced with a 20A GFCI, not a regular receptacle.
All of this is safe, except you cannot plug in the table saw.
What, you say? The table saw has a common-as-dirt NEMA 5-15 plug? How did that get there? That right there is the fly in the ointment. No, that is not safe. A 16A motor needs a NEMA 5-20 recep. (unless the motor has some very peculiar characteristics in which it's allowed to use a smaller plug AND breaker, but you do a specialized rain dance with Code to see if that is so).
However, there is nothing wrong with plugging a mix of 15A and 20A receps into a 20A branch circuit.
Make sure that if this recep is GFCI, that you either replace in-kind or move the GFCI recep to an upstream location and feed this location off its LOAD terminals. 15A Receps are supposed to be rated for 20A passthru, and that includes GFCI receps.
Short answer is yes. If your table saw motor gets pinned down and is pulling > 15 amps, you've exceeded the specs for the outlet and it will get nice and warm. This causes the contacts to degrade and eventually introduce a good fire hazard. The longer you run it over its rated amperage the more likely you are to start a fire.
I'd replace the socket with a 15/20 socket like so: https://bit.ly/34SZTvs
My table saw has similar ratings, and to be honest as long as you don't put a ton of load on the blade the current will stay less than 15 amps. I've been running mine on a 15amp socket and breaker for 8 years. Have blown the breaker a couple of times when a piece got stuck, but my house hasn't burned down yet.