Here are a few features that Google Apps Sync for Microsoft Outlook® does not support in Outlook Mail. These features either aren't available in Outlook, or they might not work as you'd expect.
Recovering deleted items
After emptying your Deleted items folder, you can't use "Recover Deleted Items" in Outlook's Tools menu to get the messages back. (This menu item isn't available.)
Sharing mailbox folders
You can't share a mailbox folder in Outlook with other users (Permissions settings aren't available in the folder's Properties dialog). This is because folders in Outlook map to labels in Gmail, which don't have permission properties.
Public folders aren't available with Google Apps Sync (they're missing from Outlook's navigation pane).
Sending executable attachments or .eml and .msg attachments from Outlook
Google Apps Sync doesn't allow sending executable file attachments (including executables in compressed attachments) from either Outlook or the Gmail interface. It's also not possible to send .eml or .msg attachments to Microsoft Outlook users hosted on a legacy Exchange environment.
Delivery receipts aren't generated in Outlook when using Google Apps Sync. If you request a delivery receipt for a message you send from Outlook, you won't receive a response when the message is delivered. However, you can select a read receipt (see below).
Read receipts are generated in Outlook with Google Apps Sync. However, your recipient must be using Outlook and must enable read receipts for their profile. In that case, you'll get a response when your message is read.
Out of Office (OOO) notifications
You can set up automatic vacation responses to let people who email you know when you're away from your mail. But you need to do this in your Gmail web interface, not using Outlook's Out of Office feature (which doesn't work with Google Apps Sync).
Learn to use the vacation responder
You can set up contact delegation in Google Apps, where an assistant can access and manage a supervisor's personal contacts. However, you can't do this in Outlook. Instead, you set up contact delegation and access a supervisor's contacts via the Google Apps web interface.
Recalling a sent message
In Outlook, you can choose Recall Message from a sent message's Other Actions menu, to try to recall a message you just sent. However, unlike Microsoft® Exchange, Gmail can't recall messages. Instead, the recipient receives both the original message, along with a follow-up message saying you wanted to recall the message.
Setting importance levels for recipients
In Outlook, you can send mail marked as "Important" or Low Priority." But these values aren't synchronized with your Google Apps account in the cloud and therefore don't show up for other users.