How and what are my rights, obligations and limitations to address and handle one employee that states another employee "smells of mildew"

Very interesting question.  I'm going to give you what will become a very complicated answer, and I can respond only in general terms.  Some people are very sensitive to aromas or odors, particularly perfumes and hair products.  Some persons experience physical symptoms when they encounter these products.  Symptoms can include headaches, lightheadedness and other symptoms which can be so serious that they render the person unable to work around the causative agent.  When these symptoms are present, the person may be unable to perform the essential functions of their position in the presence of the odor and may therefore qualify as disabled under the Americans with Disabilities Act or similar state law provisions.  When they so qualify, the employer is required to make "reasonable accommodations" which will permit the aroma sensitive employee to perform his or her job.  In most cases, the accommodation involves prohibiting co-workers from wearing perfumes, or relocating the aroma sensitive employee to a place where he or she will not be exposed to the aroma. Your case is more complicated, since 1) the aroma is not caused by a perfume or something which can be 'removed" from the environment, and 2) the complaining employee is the only one who claims he/she can detect the odor.  I think there is very little likelihood that a "mold or mildew smell" indicates the presence of any health hazard, and therefore there is no reason to require the new employee to undergo some sort of testing.  Further, such testing could well be an invasion of the new employee's privacy.  Also, the complaining employee does not contend the aroma causes any physical symptoms or effects, and it does not appear that the more senior employee us unable to perform the essential functions of his/her position due to the aroma.  Therefore, it does not appear to me that the more senior employee could be defined as disabled under the ADA, and therefore the employer is not required to make any accommodation for him/her. I think the best approach will be to tell the complaining employee that no one else detects the aroma, and that they will have to continue working together.  If the employer has the ability to move the complaining worker to a different location in the facility, that would probably be a good idea but I do not believe it is legally required based upon the facts you have provided.