Surprised to see "age" getting so much attention here. I'm not a subscriber to this ageism personally. Condition is a big factor for sure, but not age necessarily except in that age often speaks to condition.
As @Gaspare U. adeptly points out, Park Ave is very old but nobody would call it Class D. Many of the swankiest, leafiest, trendiest and most expensive neighborhoods in the U.S. are also some of the oldest and historic buildings usually hold value better than new construction. Society Hill in Philadelphia, for example, is that city's most stable real estate market, and New Orleans' French Quarter is the most expensive district in that city. Old Cambridge, Back Bay and Beacon Hill in Boston, Lincoln Square, the Upper East Side, SoHo, Park Ave, West Village etc. in NYC, Haight-Ashbury in San Francisco, Bel Air in LA, Old town Charleston SC, Georgetown DC, Capital Hill, Wash Park, Cheesman, Country Club, Belcaro, Highlands in Denver, the list goes on these are all among both the oldest and most expensive real estate locations in the country. All would be considered Class A in most people's books despite the buildings there mostly being super old. Basically if George Washington or Jerry Garcia or Jack Kerouac slept there, or if Hitchcock shot a film there, you know it's Class A. So I would say quality of construction and condition, but not necessarily age.
Median income in correlation to tenant's income, as @Mike Dymski pointed out, is a great indicator.
Surprised nobody has mentioned rent amount or just plain price yet. Higher the rent and higher the value of the building compared to the local average, higher the class obviously.
The overall character of the area is definitely a large factor as it will determine the type of tenants living there/demographics: Yoga/Orange Theory studios, Whole Foods, Starbucks, micro breweries, wine and cheese shops, public parks, bike paths, green spaces, public transportation, good schools, nice restaurants, cranes/new construction, low crime rate, high prices all indicate a Class A area whereas boarded up buildings, lots of Payday lenders/check cashing stores, dollar stores, fast food, liquor stores, homeless shelters, army recruiting centers, addiction recovery centers, industrial areas, dumps, shoes hanging from power lines, junked cars lining the streets, high crime, blight, abandoned buildings, urban decay, burnt out buildings, low prices, low rent, etc. would indicate a Class D area.
It's really pretty subjective though, I'm not sure there are universally accepted definitions but rather just people's opinions. Basically if it's a crack house that is approaching economic obsolescence that rents for less than a couple hundred/unit, then that's Class D and if doctors, lawyers, and business executives would rent there, Class A.