A speaker from the 80's will suffer from foam surround rot. This is deteriation of the foam 'ring' which connects the cone to the frame. Second item of concern would be the caps. Electrolitic caps may loose storage capability or take a memory set or even leak over time. I assume you are talking of decades here and not years.
Speaker Life
For increased clarity I am separting out this question from my other recent post. How old can a speaker be if cared for properly before one would expect some deterioration in the drivers and crossovers? Thanks