maximun number of inputs on a opamp adder circuit
The more inputs you add, the more noise the op-amp produces - this is because the noise (regard it as in series with the grounded non-inverting input), gets amplified each time a new input is added. Consider the non-inverting op-amp amplifier: -



Now, regard Vin as the op-amp input noise with respect to 0 volts but it gets amplified as shown in the formula. Regard R2 is one limb of your mixer. Every time you add a limb, R2 gets smaller and the noise on the output gets higher. For instance, if you have one input, the output noise might be X but, with 10 inputs the output noise will be 10X.

It's not normally a show-stopper but it's something to take into account and anyway you did ask!

Clearly, the sum total of all the input voltages x gain has to produce an output voltage that avoids clipping or slew limiting as well.