The most common rust spots are the rocker panels and the floors in the cargo area and near the door sills. Floor rust seems to be a much bigger problem with K5s than with pickups and Suburbans, probably because someone likely had the top off in a rain storm at some point.
Frame cracking where the steering box attaches is also common, especially for trucks that have seen a lot of offroad abuse. It's not as scary as it sounds though. A frame cracked in this area can be welded and reinforced without too much trouble.
87-91 K5s had TBI 350s. They're no LS engines, but they're simple, reliable, and they start and run consistently with a lot less tinkering and maintenance than the Quadrajet carb'd 305s and 350s that came before. Q-jets were the most fuel efficient carbs of the day, owing to the small primaries and large vacuum secondaries. But they're relatively complex. And they have a few trouble spots like throttle bushings that wear out, horns that warp when over torqued, and well plugs that start to leak with age. These things could be fixed by folks who know Q-jet carbs in and out, but that's a dying breed. And you're not likely to make a bad one good with tinkering and the kit you get from Autozone. If you buy a carbed version and you can't get it to run consistently after a lot of cleaning and adjusting, toss the Qjet in favor of an Edelbrock 1406.
In the early 80s GM introduced ESC. It involved a knock sensor and a computer module that would pull all of the timing out of the HEI distributor to prevent detonation. At the time it was a great way to allow GM to increase compression and eek out a bit more power during the days where lean tuning for emission controls made it difficult to control engine knock. After so many decades, the module goes haywire and starts to retard timing randomly. If you get intermittent slow down, where the truck doesn't seem to misfire but abruptly loses all power and cannot seem to maintain any speed above about 50, the ESC is suspect. You can bypass the ESC system with a couple of wire splices at the HEI distributor.
Vent windows are nearly impossible to keep from whistling. Replacing the vent window weatherstripping is a monumental task, and often the replacements seal worse and whistle more than the ancient originals. Best bet is to replace the latch and rubber beneath the latch so they close as tightly as possible with the original weather stripping. As for the remaining windows, GM used a type of white grease that turned thick and hard within a couple of decades. Lots of people replace window motors only to find the window still operates very slowly and the new motor quickly dies. If you tackle the window motors, be sure to spend A LOT of time cleaning up and relubing the window regulator, tracks, and rollers. Also, if you tackle this job, be sure you know what you're doing beforehand. The window regulator is basically a heavyily sprung, large pair of scissors. There are tales of people losing fingers when removing the window motor from the regulator without first doing something like drilling a hole and inserting a bolt to make sure the regulator won't move.
Mechanical auto-locking hubs from the 80s are likely useless by now. So, replace them with Warns. The 10-bolt rear axle with the gov-lock limited slip is nicknamed the "gov bomb" for a reason. 10-bolt open diffs are a lot less likely to explode, and the axle shaft will generally hold up with 35" or smaller tires. The solid front axle is either a Dana 44 or very similar corporate 10-bolt, depending on the year. They're pretty bullet proof, as evidenced by the fact that they developed 10-lug outers for these same front axles and used them in the 1-ton trucks.
The 700R4 transmissions are weak. They also suffer because a lot of those trucks came with 2.73 gears in order to meet CAFE standards. A 5000 pound truck, with 2.73 gears, trying to maintain OD and keep the converter locked in the days of 55 mph federal speed limits? So stupid. If you have a 700R4, drive it till it fails and swap for a TH350.
Other than that, you'll just see a lot of wear, tear, and failures that would be common to any 25-40 year old vehicle. Parts are plentiful and mostly inexpensive. And the trucks are really pretty simple and fun to work on.
[This message has been edited by North Dallas Forty oz. (edited 7/24/2014 1:57a).]