We are a Google Apps Reseller.
The two most successful tools we have seen our customers using are: shared Google Spreadsheets and Trello.
The spreadsheet might seem crude but it is very flexible in how you set it up, it can be sorted and comments can be inserted. This would be the quickest for you to start using right away. Depending on the complexity and quantity of the tasks, you might want to look at Google Apps Script for automating your work with the tasks in the spreadsheet.
Trello is a really cool app made by the same folks that built StackExchange. It does not integrate with Google Apps directly but you can use your Google login (nice to not have to remember another password). Additionally, if you want to get more complex, it has an API which can be manipulated with Google Apps Script.
We have seen both work successfully in Google Apps environments. Take a look at each to see if either will work for you.