We have a directory called “Whom to contact about what.” A couple (that is exactly two) co-workers have come to me and told me that is should be “Who to contact.” I was taught that the ‘rule of thumb’ is in any case that you would use him or her, you use whom, so you wouldn’t say “I’m going to contact he” and therefore it should be “Whom to contact.” I tried a couple of online grammar checkers, and neither was marked as incorrect. So, who is right? (Him is right? I don’t think so ;) )
Primarily, you can approach this grammatically or stylistically.
Technically, whom is right. In your phrase it is the object of the verb to contact. But there are lots of reasons why "Who to contact" is far from egregious. In fact, stylistically, lots of folks would consider "Whom to contact" stuffy, bookish, or formal. Are they wrong?
Lots of people employ who indiscriminately where both who and whom are possible, with different meanings. But, how could anyone possibly confuse the who as the subject of this verb, especially a verb in infinitive form (which is used in English when an overt subject is impossible)?
In your longer phrase "Whom to contact about what," I think the length of the phrase and the additional object of the verb make it sound less stuffy than it would sound in the shorter phrase "Whom to contact." If it doesn't bother you to sound stuffy, or if you want to communicate distance, then go with whom. If it is important to be colloquial, or if you want to communicate friendliness and helpfulness, then go with who.