I have came across two questions on the topic, however they both seem to assume that mouthwash is beneficial.
Is mouthwashing beneficial?
Medical Sciences Stack Exchange is a question and answer site for professionals in medical and allied health fields, students of those professions, related academics, and others with a sound understanding of medicine and healthcare-related sciences. It only takes a minute to sign up.Sign up to join this community
Apparently, yes fluoridated mouthwash seems beneficial against carries, at least in children. ADA says:
Fluoride ions, which promote remineralization, may be provided by certain mouthwashes. A Cochrane systematic review found that regular use of fluoride mouthwash reduced tooth decay in children, regardless of exposure to other sources of fluoride (i.e., fluoridated water or toothpaste containing fluoride).
[citing:] Marinho VC, Higgins JP, Logan S, Sheiham A. Topical fluoride (toothpastes, mouthrinses, gels or varnishes) for preventing dental caries in children and adolescents. Cochrane Database Syst Rev 2003(4):CD002782.
Mouthwashes also seem to help with gingivitis, although which active ingredient is best/responsible for that seems less clear:
When used in mouthwashes, antimicrobial ingredients like cetylpyridinium, chlorhexidine, and essential oils have been shown to reduce plaque and gingivitis when combined with daily brushing and flossing. While some studies have found that chlorhexidine achieved better plaque control than essential oils, no difference was observed with respect to gingivitis control.
Frankly that seems more controversial, as the meta-analyses cited (by ADA) for the latter seems to have had some comments/correspondence. I didn't follow the exchange.
The NHS recommends against using a mouthwash with chlorhexidine for longer than 4 weeks because of the staining it can cause.