Syncing Mail with Gmail
There still seems to be some issues syncing Apple Mail with Gmail. This was definitely a big issue when Mavericks was first released. About 3 weeks later Apple released an update to Mavericks, that appeared to fix the problem. After over a week of testing with the up date installed, it appears that the sync process is still very slow. In Mail open Activity (Menu->Window->Activity) and observe all the sync processes with Gmail) At times the sync process goes on for several hours. Hopefully others will report their experience here.
iMac, OS X Mavericks (10.9), MacBook Air, IPad v1, Apple TV v2