Liverwort is not an easy weed to eliminate, though it is interesting to learn more about. Here is the text from an earlier "ask an expert" response "Once any unwanted growth such as liverwort gains a strong foothold, getting rid of it means war. So, consider yourself a General in charge of Operation Eradication. The battle must continue for an extended period, likely several years, because you have a “spore bank” of sorts which will continue to germinate and produce more liverwort. Always remember that you are in charge of winning! Liverwort has long been a serious problem for large-scale growers of container plants. Research showed that drying the surface, then mulching, limited it. Nowadays, that's the reason many pots are mulched with ¼-10 gravel or filbert shells. This strategy will work: - As much as possible, allow the soil surface to dry. Perhaps water less often, but longer for each session, so that your desirable plants continue to thrive. - Use fertilizer judiciously, reducing the amount you use and, when you do use it, place it around individual plants that need it, then lightly scratch it into the soil. - Because liverwort has shallow roots, it’s easily scraped off the soil surface; then add an inch or two depth of mulch of your choice. - Repeat the above as needed, while realizing you must be persistent. It’s important to know that most herbicides won’t work. The reason: liverwort isn’t a vascular “plant.” Then, too, no home-use products are labeled for liverwort."
This is written for commercial operations, but is helpful information: "Liverwort" from the Oregon State University Department of Horticulture, http://horticulture.oregonstate.edu/content/liverwort-0