How do you upgrade tables that are way out of date?

I have a hosting customer that has been upgrading wordpress as new version come out, but due to an problem unrelated to wordpress, the tables have not been getting updated along the way. So now they’re running the latest WP (3.05) but with really old tables. I don’t know when the tables were last successfully updated… but there’s no commentmeta table, which I understand was added several versions back.

I’m surprised that the site isn’t spewing any errors with the tables not being up to date. Anyhow, I’m looking for recommendations on how to get their table versions in sync with their WP version.

One idea I had was to back up their data and install a very old version of WP, that points to these same tables, and then incrementally upgrade to the latest version so that each table update gets applied. Or, is there some other procedure for forcing WP to bring tables up to date?