I led a team to develop a weed identification wheel for use by people who don't have a lot of background in weed management. Since space was limited, I had to narrow down the list to the top 12 weeds in landscapes and gardens and to do this I presented a longer list to people who do work with weeds in San Diego. We came up with the following: yellow nutsedge, stinging nettle, annual sowthistle, bermudagrass, black nightshade, clovers/medics, crabgrass, oxalis (woodsorrel), dandelion, poison oak, purslane, and spurges.
Now before you start commenting that these are not your top 12, recognize that these are what many professionals and home gardeners in San Diego area do consider problematic. What I would like you to concentrate on is what is on the list, namely yellow nutsedge and poison oak. Poison oak is undoubtedly a California native while the heritage of yellow Nutsedge is a bit more muddied. Calflora has two varieties of yellow nutsedge listed Cyperus esculentus var. leptostachyus which is not a native but listed as being found in only in San Diego County and C. esculentus var. macrostachyus which is native but surprisingly Calflora does not have any records in California. There are at least two other C. esculentus varieties listed but I will leave it to the reader to follow up on this. If you are one of those kinds of people, I suggest you take a look at “A Revision of the Infraspecific Taxonomy of Cyperus esculentus (Yellow Nutsedge) with an Experimentally Evaluated Character Set” (http://edepot.wur.nl/215596) by Schippers et al.
Anyway, I diverge. We got some blowback from some members of the California Native Plant Society by putting the two above mentioned plants on the weed identification wheel. Apparently if a plant is native it can do no wrong. I'm afraid I have to disagree, but with disclaimers. Certainly if a native plant is growing where it is supposed to be growing, for example poison oak growing in woodlands, than of course it is not considered a weed even if someone does happen to brush by it while hiking and get dermatitis. However, if it's growing up a chain link fence next to a school, for sure I would expect that we would want to remove it.
Yellow nutsedge is a ‘B' rated pest in California ["B" - A pest of known economic or environmental detriment and, if present in California, it is of limited distribution. B-rated pests are eligible to enter the state if the receiving county has agreed to accept them. If found in the state, they are subject to state endorsed holding action and eradication only to provide for containment, as when found in a nursery. At the discretion of the individual county agricultural commissioner they are subject to eradication, containment, suppression, control, or other holding action] although CDFA does not differentiate among varieties. Other weedy plants that are natives include stinging nettle (Urtica dioica [although some subspecies are not native]), and many dodders including western field dodder (Cuscuta pentagona).
The point is, weeds can be native or introduced. There are many definitions of a weed and one that I believe applies when deciding whether a native plant should be considered as a weed is if the plant in question is growing outside of its native habitat, e.g. a nursery , sports field, or cropland, and interferes with production in agriculture or other cosmetic or recreational sites or uses.