What words are considered controversial? To be quite blunt, words related to sex and other untoward bodily functions are probably off limits. Words related to violence or racism, or which are just plain macabre may not be good candidates as well. I have seen a few examples of these words in the past; the most visible example was Wendy Guey's winning word in the 1995 national bee: vivisepulture, which means "the act or practice of burying alive." But by and large, it's reasonable to consider such words verboten. I've not seen any words that might be considered controversial appear in any bee for years.
There is a question about words about alcoholic beverages. I've heard rumblings that perhaps these words have begun to be phased out of word lists because of concerns that they might be inappropriate themselves. I do not believe that using such words actually promotes an alcohol-laden lifestyle. This is especially true since such words have been so common in American culture since...well, since the founding of our nation itself. In the past, I've seen words like zwetschenwasser, zinfandel, jeroboam, and daiquiri used by Scripps. Indeed, even the word julep is part of Spell It, appearing as an Arabic challenge word. If we take a step further into the realm of controlled substances, the words psychedelic and barbiturate come up. All of these words are found in the Consolidated Word List. So I would consider alcoholic beverages and related words fair game.
Aside from the above paragraph, I find this post difficult to write. It's not easy to indicate what words to eliminate without stating them outright. And if I were to actually do so, this post itself would become controversial and potentially inappropriate. Perhaps the best way I can state it is this: use your good judgment. If you think the word might be inappropriate, it probably is. Or more to the point: if you think the Scripps word panel and judges might think a word is inappropriate, it probably is. Scripps has a strong interest in running a smooth, fair, and challenging bee program, but they have no interest in attracting controversy...and who can blame them? So stay away from controversial words, just like they would.