I've got a P from a very near year. Not much to watch out for. The stock pups are just ok, and most folks seem to upgrade them. Also, after 23 years, changing out the electronics is an accepted, but cheap-and-easy fix. After re-wiring my P several times and putting in a new pickup I'm finally switching out the electronics. Better quality pots and such aren't expensive, but if you don't want to do alot of work, GFS will sell you a very affordable pre-wired harness that is probably about on par with what it originally had installed. Invalid Link Removed Nothing special, but a solid affordable choice.
Aside from rather pedestrian hardware, the biggest bad is probably that alot of these early MIM instruments have fingerboards that are half the thickness or less of most guitars. My bass has a board so thin tha the marker dots half in the fingerboard half in the neck. This isn't necessarily a terrible thing and does make the neck thinner front-to-back, but it's worth noting.
Lastly, I always recommend that anyone with a jazz bass and a bit of DIY inclination install a series-parallel push/pull pot to increase the tonal options available to you.