Plants
In general, the plants will need weeding only if any seedlings happen to appear, and pruning only to keep them healthy and in shape. If any are tied against a wall, check the wires and nails periodically, to make sure they are not pulling away, and tie in new shoots. Occasionally, especially if the plants are protected from the rain, wipe any build-up of dust from the leaves; if dust is allowed to remain, it will interfere with photosynthesis, and the growth of the plant will be slower. As a matter of routine, remove dead leaves from the plants before they begin to rot.
Floor Surfaces
The balcony is probably the easiest to maintain, because, by its very nature as an extended part of the living area, it is usually easy to sweep clean or wash down.
Decking will need to be brushed with a stiff brush to remove any algae; then treat with an algae killer. In addition, treat softwood decks with a preservative every year.
Wash tiles periodically to reduce any build-up of algae; relay any tiles that work loose before they crack.
Concrete tends to suffer most damage from small cracks. If you overlook or ignore these, the action of the weather, or a stray seedling that grows in the crack, can enlarge it and cause considerable damage. Chip away loose material and repair the hole with a stiff mixture of concrete containing an adhesive.
Regularly rake any gravel level; it should not need any other attention.
Seating
Bring the cushions from upholstered furniture inside during wet or cold weather and clean them according to the instructions. Wash plastic frames with a detergent solution periodically to remove the water marks left by rain.
Metal furniture can be left outside but it will need a scrub in spring with a detergent solution, to remove the dust and deposits of the winter. It will benefit from a new coat of weather-resistant paint every two or three years.
Treat softwood timber seating with a preservative or new coat of varnish every year. Hardwoods, Such as teak, do not need preservative. A rub over with white spirit, soap and water and, finally, teak oil will protect them for the year.
Containers
Most containers will need little maintenance. Weathering tends to enhance their appearance rather than detract from it. Any that have been painted may need another coat, and reconstituted stone containers may need to be brushed down.
Trellises and Pergolas
Particularly where the trellis has been erected as a windbreak, the means of support will need regular checking to make sure it is still rigidly in place. The bottoms of posts are prone to rot. Treat them with preservative but, as many wood treatments are toxic to plants, it is usually better to detach the plants from their supports, and protect them before you begin applying the preservative.
Railings
Rub these down and repaint them with a weather-resistant paint when they show signs of damage.
Electrical Fittings
If electricity has been connected to the roof garden, for lights or a pond pump, it should be checked every year for signs of wear; this is best done by a qualified electrician, who can replace any damaged cables or connections.
Resources:
Green Roofing - Guide to green roofs.