Just posted this to Apple Support:
Error: Recurring events appear multiple (ie several hundred) times on the iOS 6 device until eventually all free memory of the device is eaten up and it stops working.
Device: Any iDevice with iOS 6.x (6.0 and 6.01). iOS 5.x not affected.
Software: iOS Calendar app synced with Google Calendar (either as part of a synced GMail account or individually as CardDAV account). Google Calendar (either GMail or Google Apps account) with subscribed Birthdays and Anniversaries Calendar (i.e. calendar showing birthdays and anniversaries from all contacts stored in Google Contacts). "Ordinary" calendar events, including repeating / annual events entered manually in the calendar, fo not cause the bug.
The bug *may* affect other types of calendars, but as I do not use any, I did not check (e.g. iCloud, Yahoo, etc.).
Symptom: Recurring events (from the Birthday Calendar only) appear multiple times in the iOS calendar app. They do not show the colored dot next to them indicating the calendar they belong to until the event is opened in iOS Calendar. Disabling the respective calendar in Mail&Calendar settings does not always remove these calendar entries. Eventually, calendar entries are multiplied so many times that all the iOS device's memory is eaten up (i.e. several gigabytes) until an Out of memory error message appears. Sometimes memory apparently gets so corrupted that the device cannot be synced with iTunes any more and has to be reset to factory state.
It is yet unclear what causes the multiplication of events, as often the events are shown only twice or a few times for extended periods of time and only days later they multiply to the hundreds. The actual calendar on google.com remains unaffected.
Remedy: None (other than stop syncing the calendar).
Bug Status: I was able to recreate the bug with different GMail and Google Apps accounts on my iPhone 3GS and iPhone 5 as well as several iPad mini's in the local Apple Store.
Extensively discussed the bug with Apple Care (Germany). Apple Care could not help as they cannot use non-Apple products, in particular have no access to GMail accounts and therefore cannot recreate the bug.