Diodes, their use in mixers and taylor approximation
There's two easy ways to answer your question: 


Add another term to the Taylor series and evaluate it in either a computer algebra system (Mathematica or Maple or Maxima) to find when the higher-order terms become significant.
Simulate your circuit under transient analysis in a SPICE-like simulator, and look for higher-order terms.


Keep in mind that when "unwanted" terms fall well outside the desired output band (for example, \$3\omega_1\$, \$2\omega_1+\omega_2\$), they'll be relatively easy to filter out. The terms that cause practical problems are the ones that fall near the desired output band (for example \$3\omega_1-\omega_2\$, assuming the input frequencies aren't widely separated)