If the continuous variables are measured with error, can the use of dummy variables mitigate the problem? For instance, IQ measures intelligence with error. So will using a dummy of high, medium, low IQ mitigate the measurement error problem? Thanks!
Dichotomizing predictor variables actually reduces power to detect relationships between a continuous predictor and the response variable. Royston (2006) is one of many articles citing this as a reason why dichotomizing is a bad idea.
You can see @gung's answer to this question highlighting even more problems, such as hiding potential nonlinear relationships, among others.
What matters is the magnitude of an error multiplied by its likelihood. When a noisy continuous variable is dichotomized, the magnitude of an error is huge because the error is to put someone in the wrong category - a 100% error. http://biostat.mc.vanderbilt.edu/wiki/pub/Main/BioMod/catgNoise.r is a script that can be run in RStudio (it requires the R
Hmisc package also) that provides an interactive demonstration of the fact that no amount of noise added to a predictor can make dichotomization have better power than analyzing the variable continuously - even when the relationship is nonlinear (but monotonic) and one improperly uses a linear fit.
The idea isn't even intuitively appealing (at least to me): using a discretized version of an accurate measure might be preferable to using a continuous version of an inaccurate one; but how on earth is discretizing an inaccurate measure supposed to improve it? The situations in which it might are those in which the truth is discrete, or close to it: in your example, that people really are dumb, or ordinary, or smart, & nothing in between; & that IQ is a measure from which you can predict membership of those three classes. Note that still wouldn't justify binning IQ scores into top third, middle third, & bottom third; you'd need an idea of the proportions in each class, & the whereabouts of the cut-offs. The general message from DeCoster et al.'s simulations is that discretization is only ever justified by quite specific prior knowledge about the distribution of the underlying variable being measured.
MacCallum et al. (2002), "On the Practice of Dichotomization of Quantitative Variables", Psychological Methods, 7, 1
DeCoster et al. (2009), "A Conceptual and Empirical Examination of Justifications for Dichotomization", Psychological Methods, 14, 4
It really depends what you mean by mitigate. It is not always a bad idea to bin the data. You are throwing away information when you do this but sometimes that is made up for by allowing for a more tractable model. An example would be binning data so that you can use the Chi-square test or a Chi-square minimization routine or are somehow trying to take advantage of the central limit theorem to mitigate the fact that you may not have a good handle on the distribution of the noise.
However if you do this, be aware that you are throwing away some information and that there are often other ways of using the data without binning. But if you cannot figure out how to model things without binning then go ahead and do this. If you think of a better, more sophisticated method later then revisit it.