The claim: Spirulina lowers LDL (bad cholesterol) and raises HDL (good cholesterol). It can also reduce the incidence of certain mouth cancers and reduce blood pressure. It also reduces nasal stuffiness in people with allergies. It may also enhance exercise endurance and reduce blood sugar levels in diabetics.
The science: Each one of the claims above is supported by at least one study. Only the study about nasal stuffiness was poorly designed.
Caveats: The number of studies are few, but other than the nasal stuffiness study, they were well-designed.
My recommendation: With no evidence of harm, supplementing your diet with Spirulina may make sense to help with the problems mentioned above.