I have a similar but not identical problem. In your case the alert is getting duplicated within the event. In my case I get two alert boxes popping up at top right of screen but there is only one alert (default) set in the event. If I double click on one of the alerts it takes me to the event in the calendar. Double clicking on the other alert takes me nowhere. This seems to be happening for events I create on my Macbook Air but not for events I create on my iPhone which are sync'd to this calendar. I'm also getting single alerts for events I deleted some time ago or which I have in an old gmail account which I am not using anymore. I thought maybe there were two identical events stacked on top of eachother but that is not the case as I can delete the event and there is not another below it.
This happened after updating to Mavericks. I am getting 2 alerts on my calendar desktop for the same event each time an email comes in that has a calendar event. Anyone know how to stop this? To be more precise, I belong to several meetup.com groups and everyime an email comes in about a new event, I get 2 of the same popup alerts on my desktop calender asking if I want to add the event.
I also have issues where my gmail account stops syncing email to mac mail, but will come in to my iphone. If I restart mac mail, then it will bring in my gmail emails again. Again, new since Mavericks.
Any help is appreciated.
I solved my double alerts problem by deleting my old gmail calendar. I had imported the calendar into Apple Calendar and then disabled the gmail calendar by unchecking the box next to it in Apple Calendar so the events did not show up on the calendar, but the alerts were still appearing. After I deleted the calendar the alerts stopped so now I only get an alert from the imported event in Apple Calendar.
Gmail and mac mail don't play well together! There is a good discussion here and Steve's Fix worked for me, particularly stopping mac mail from saving drafts to the server.
I figured out how to solve my specific problem and it was not Gmail. Because I had a smart mailbox, I was getting the email notification twice, once from the inbox and once from the smart mailbox. Deleted the smart mail box and now only one notifcation per email. Was not happening until Mavericks, so another thing for Apple to work on