In theory, the authority to approve an LSA manufacturer and design has the right to audit their testing and work. What I'm interested in how often does this happen in practice, and whether there have been any cases of violations found because of this. Is the system of trusting manufacturers to be honest with their paperwork working so far?
Per this letter it appears that manufacturers who make LSA compliant aircraft are subject to a sort of enforced self regulation. Basically, they are required to audit themselves every year and are told that the FAA could come and inspect their facility at any given moment, with heavy fines if an inspection is failed.
On top of this each aircraft itself is inspected by a technician before it leaves the facility to make sure that each aircraft meets the standards.
I did a bit of a search over a few of my favorite LSA news sites and I couldn't find any instances where an FAA inspection actually resulted in the proposed fines/punishments. It seems that so far the semi-self-regulation model is working fairly well. Well enough that, as Dan Johnson points out in that second article, it appears the FAA is considering using the same certification model for type aircraft as well.
To summarize, yes they are being audited, but by themselves. It is also likely that outside bodies are auditing them as well, but nothing newsworthy seems to have come of any random inspections, so there is no mention of said audits. I'm sure if somebody fails one, it will be big news.