For analog summing and multiplying, what would be the disadvantages of scaling down voltages of input?
There is no particular serious problem with this approach. The inputs don't need to stay within the supply voltage range if the series resistors are high enough (though you do need to worry about what may happen if the input is connected to an external voltage and there is no supply voltage- the summing junction will no longer be at virtual ground and current will flow somewhere). 

You can calculate the voltage and current noise as usual, high value resistors will have greater Johnson-Nyquist noise, and the noise current of the amplifier will have more influence, but neither is normally much of an issue. 

It may be necessary to add some capacitors in the resistor ratio if you have very high value resistors (to get flatter AC response, increase stability and decrease noise).