The most reliable method for dating a Ball Mason jar is by looking at the logo. The logo changed frequently until 1962. A handy chart to help identify Mason jars by their logo is available on the Minnetrista website.
Vintage Mason jars sometimes can be identified by their color. Some old jars are a variety of colors, most often light blue. Antique jars feel thicker and heavier than modern jars as well. Because manufacturing was less reliable, old jars often have imperfections that are rare in modern jars. Dates printed on the jar and mold numbers have nothing to do with the age of the jar, and they are not accurate ways to determine if a jar is antique.