Containers should have more drainage than normal, drill some holes if need be. Air circulation is also advisable, moisture is not only soil borne - it is air borne so ample ventilation / air circulation is advisable.
Aphids and spider mites will atatck any plant and kumquats are on their menu. Snails and slugs on occasion will chow down on the foliage, but they are rarely a major issue. Leaf rollers - from timwe to time will appear on kumquat trees but are also seldom a major issue. Scales can be a general nuisance. If scales are detected and natural organic methods of control fail, Neem is the most effective control for scales and ecologically sound as well.
Citrus does not lend itself well to being root bound or 'pot-bound', in fact that is why you'll rarely see bonsai as a citrus plant, Kumquats are no exception. They can be grown successfully in containers, but you'll need a relatively large container with more than ordinary drainage holes. Once the tree is established, elevating it slightly off the ground is advantageous not only for drainage but air circulation as well.
If you live in a zone where it isn't necessary to move the trees indoors in cool weather, it would be advisable to provide some protection for the semi-exposed roots that the containers facilitate. Some plastic or even a blanket should suffice.
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