Definition of a Weed

Surveying my backyard here, I've identified a number of weeds that will have to go: English ivy, English holly, blackberries, broom, buddleia. But a brochure entitled "Weeds of Blue Mountains Bushland" suggests that I've got more problem plants to deal with than I thought. Cotoneaster is one, particularly C. franchetii and so is Himalayan honeysuckle (Leycesteria formosa). The dogwood, Cornus capitata, that I was initially delighted to have turns out to be invasive here, as is Prunus padus, the Bird Cherry. The latter is aptly named, attracting King Parrots and Crimson Rosellas to our garden, as well as smaller, less brilliant birds like honeyeaters and mynahs. Trouble is, the birds then disperse the seeds in the surrounding bushland and the resulting seedlings rapidly displace native plants.
Being a responsible gardener, I will get around to having all these thugs removed, which will leave me with some rather nondescript hydrangeas and not much else. Still, there are some gorgeous Grevilleas and Banksias that I can plant instead, and a range of non-invasive "exotics", including roses, that I can grow without guilt.