1988 was the first year for the 1500. I had a 1990 which was a good bike for it's purpose. Very comfortable for passengers. Keep a close eye on the temperature gauge. If the temperature rises quickly on slow riding, the radiator is probably coated up internally and needs to be replaced. The cooling fans will come on a lot any time you ride in town, but should never come on while on the highway. Batteries don't last very long, they have a hard life with all the electronic goodies and more so with accessory lights. If you know the cooling system is good, higher engine temperatures will result when the battery is in poor shape. This is because the alternator is working harder than normal to carry the bad battery.
You may want to change the front springs as the stock spring rate is marginal. Changing to progressive rate springs will help a lot. These bikes are not much fun to work on, it takes several hours to replace the air filter since it's located under the radio. Check the clear plastic tube (left side) behind the cover near the footpeg. Remove the plastic plug; only a small bit of moisture should come out. This is the drain tube for the condensation catch tank above the engine. You risk engine corrosion if this tank is not drained often.
The caburetor is buried deep and you will get some fuel percolation on hot days. The fuel injected GL1800 is a probably a better bike in this regard. I haven't ridden an 1800 so I don't know how they compare overall.