Roofs need to be monitored as Jon points out. There are quite a few posts in Repairs and Maintenance on taking care of both rubber and metal roofs.
Brakes and bearings need regular attention, regardless of age. Clean, inspect, and repack bearings annually in the spring. More often if you put a lot of miles on each year. Brakes should be inspected, lubed (yes, there are lube points in drum/shoe brakes) and adjusted annually.
Brakes should be tested regularly. A low speed, hard stop on gravel will quickly tell you if the brakes are doing their job. While you have the trailer off the ground doing bearings, etc., after you put it all back together, plug it into your tow vehicle and test the brakes on each wheel. Good time to adjust them, too. If you don't get fairly uniform braking on each wheel, the electric portion of the brakes may have a problem. Most common is wiring issues: corroded or oxidized connections, damaged or broken wires.
The bushings in the suspension mounts tend to wear out. If your budget allows, there is a wet bushing upgrade that is just super.
There are a number of detailed threads in Repairs and Maintenance that should answer almost any question in regards to brake, axle, and bearings maintenance.
Dexter was the most common axle and brakes in TT's in the '90's. www.dexteraxle.com
for all kinds of info. Be sure to download their complete manual on brake/axle/bearing maintenance. Even if you don't have Dexter, their service manual is an absolute bible for this maintenance. http://dexteraxle.com/i/u/1080235/f/...anual_2-08.pdf
Any electric component can fail, but those on the outside of the trailer are especially prone to corrosion or oxidation issues. I keep a small tube of dielectric grease (available an any auto parts store) handy, and use in on any connection that I work on. Light bulb sockets, the 7 pin TV connector (both sides), etc., etc. all will benefit from a coating of dielectric grease. Living in upstate NY, we have to contend with salt on the roads for 5 months a year. My 7 pin on the TV is liberally slathered with the grease.
I am not sure which exact marker lights your unit uses. You'll want to find out which bulb they use, and keep a stock on hand. The marker lights are prone to water damage over time and should be checked regularly.
Keep some 1157 bulbs on hand for the stop/turn/tail lights. Dielectric grease on the base and contacts helps there, too.
I would encourage you to read back through the various threads in this forum and in Repairs and Maintenance. Over the past three years, almost every conceivable topic has been chewed on quite thoroughly. I have been trailering since the early 1970's, and I still find new gems by reading back through the threads.