I would start with the simple thing first and find out why the car is shaking and get that taken care of. Hopefully you have a reputable tire shop you trust. Have them balance the tires and take a look at the front end and brakes for anything worn.
This may take care of the mirror shaking.
I am not familiar with the construction of the Versa mirror and have nothing concrete to offer as to how to tighten it if that is indeed what it needs.
On a somewhat related note, I have a Toyota Tundra that had the shaking mirror on both sides. On that vehicle, there are two or three screws on the bottom of the housing that when tightened, fixed the loose mirror issue. May want to look at the bottom of the mirror housing.
This may take care of the mirror shaking.
I am not familiar with the construction of the Versa mirror and have nothing concrete to offer as to how to tighten it if that is indeed what it needs.
On a somewhat related note, I have a Toyota Tundra that had the shaking mirror on both sides. On that vehicle, there are two or three screws on the bottom of the housing that when tightened, fixed the loose mirror issue. May want to look at the bottom of the mirror housing.