I had an issue with calendar alerts and badges for my Gmail calendars synced to my iPhone 4 (iOS 4.3.3) not working. They had been working for a time prior.
To fix the problem, I went into "Settings", "Mail, Contacts, Calendars", "Gmail", and turned off the Calendar. I deleted the calendar entries off the iPhone when prompted. I then turned back on the Calendar in Gmail settings.
After doing this, open up the calendar on the iPhone. Select the "Calendars" button in the upper left corner, and enable the main calendar by selecting it. All of my calendar event showed back up but the invite badge would not appear. I rebooted serveral times; deleted the profile and re-added utilizing Microsoft Exchange - see http://tinyurl.com/3efv392. I then noted that MobileMe (Find My iPhone) was inactive; I activated,rebooted and all alerts are working again.
Appears to be an issue with Gmail Exchnage sync and MobileMe; a few days later I noted I was receiving Gmail calendar emails but no badges. I checked under Mail, Contact, Calendar on my iPhone and sure enough MobileMe was inactive again (I did not turn it off). I re-activated; rebooted and the Gmail invite notifications for all my calendars began working again.
Hope this helps.