Let's say I am running a regression in which my dependent variable is homicide and my variable of interest is access to violent videogames. Let's say that I also throw in the kitchen sink with regard to my control variables-- I have 38 demographic controls, 30 criminological controls that may or may not be relevant, and so on. Some of these controls may even contain fuzzy or bad data (typographical errors, blank cells, and so on). What are some of the negative consequences of these sloppy regressions?
I was told by a grad student in Statistics that these controls will have no effect on the p-value between the dependent variable and the variable of interest, even if the coefficients on the controls will be senseless. But if this were true, why don't all academics just throw in the kitchen sink in their regression? Is it possible to the p-values to become smaller through the addition of junk controls?