Degredation of Anusol and Sunscreen
Existence in an oxidative atmosphere means many commercial products may be, and often are, exposed to oxygen.  Many things, and almost all drugs, react with oxygen.  The products of these reactions (oxidations, normally) are different molecules that may be less effective than the original drug.  As such, the efficacy of a drug that is beyond its expiration date is presumably lower, meaning dosing instructions become invalid.  Similarly, water content in the atmosphere may alter reactivity of drugs.

In general, studies to determine expiration dates take large amounts of time, and are hence expensive.  The standard for such an expiration would normally be a remaining purity level of the drug in question.  For example a company might study their drug for a year and note it is still 99% unchanged.  This means it meets a pretty good standard after one year.  From a marketing perspective they just label the drug as expiring after one year.  This allows them to be out of the legal liability because they are disclosing actual data indicating the efficacy of the drug over a period of time, and if a consumer takes the drug outside the expiration date, they are using the drug counter to instructions.  It also tends to generate extra sales for people who keep old drug stocks around, and must buy new ones to guarantee efficacy.  The actual drug may be still therapeutically useful even if "expired".

Specifically related to zinc oxide, I see no pathway for further degradation.  Wikipedia reports Anusol actually contains zinc sulphate (monohydrate), which I expect to be similarly robust.  However, the other but the qualities of the product ( presumably an ointment or lotion ) may have degraded such that its application may be less effective.  Additionally the Anusol plus contains a drug called Pramocaine Hydrochloride.  This compound is likely to oxidize overtime.