GitHub User: bradrobertson
I'm the author of the Apartment gem that's referenced here. We've been using it for over a year on Heroku and it utilizes schemas.
It's definitely fine to use, we still get great performance with well over 100 schemas in an application with 50+ tables per schema.
The article mentioned by @4ware talks about issues with heroku's pg:backups command. (I'm pretty sure that article came about from our support queries to them)
It DEFINITELY has issues, but this is not a shortcoming of Postgresql, schemas or multi-tenancy with schemas, but rather the heroku tool itself. Now that Postgresql has ingres support on their dbs, you don't really need to use their built in tools. We just pg_dump when we need to and it works just as fast as one would expect.