View last successful mail check/sync
I do not think you can view a log of some kind in the ui, however you can always manually sync and the icons show if it was successful.

Settings &gt; Accounts &amp; sync &gt; Manage accounts &gt; your account &gt; OPTION BUTTON &gt; Sync Now



this is in android gingerbread version


You will see the spinning icons appear then disappear when synced, then you know :) 

I think I remember seeing widgets that sync your accounts in one click so it may be worth exploring the app markets.