Shortly after Mavericks/OS X 10.9 was released users that configured Apple's Mail.app to receive their Gmail universally complained about several bugs.
Mail Update for Mavericks 1.0 includes "improvements to general stability" and compatibility with Gmail, including the following:
Fixes an issue that prevents deleting, moving, and archiving messages for users with custom Gmail settings
Addresses an issue that may cause unread counts to be inaccurate
Includes additional fixes that improve the compatibility and stability of Mail
PowerPage's Tom Hesser notes that "Mail... inched from version 7.0 build (1816) to 7.0 build (1822). While the number treatment makes this seem like a minor patch to Mail, it will probably be a big deal to anyone who has been wrestling with Mavericks’ Mail program and their Gmail accounts."
As with any software update, Apple recommends you make a full backup of your system, preferably using Time Machine, but you can also use a system cloning tool if you have one. CNET's Topher Kessler deftly notes that this update may have unexpected results if you have third-party software installed that affects it or the operating system. Examples of such software could be third-party spam filters and plug-ins for Mail and related services, even firewalls that might interfere with network connections that Mail is trying to make.
I have three Gmail accounts configured in Mail for Mavericks, but haven't noticed any issues before or after installing the update. It appears that the majority of accounts that were affected were of users that had heavily customized Gmail's IMAP settings.