I recently setup a User Profile Synchronization service to sync with AD and then use BCS for supplemental profile properties.  I ran into several issues with the User Profile Synchronization service.  Here are a few errors and the solutions for them...

<strong>Events 1001, 1004, and 1015</strong><br />
    <p style="padding-left: 30px"><strong>Errors</strong>
        <p style="padding-left: 60px">
           &bull; The resource 'C:Program FilesMicrosoft Office Servers14.0SQLDatabaseSettings.sql' does not exist.<br />
           &bull; The resource 'C:Program FilesMicrosoft Office Servers14.0ServiceMicrosoft.ResourceManagement.Service.exe' does not exist.<br />
           &bull; Detection of product '{90140000-104C-0000-1000-0000000FF1CE}', feature 'PeopleILM' failed during request for component '{9AE4D8E0-D3F6-47A8-8FAE-38496FE32FF5}'<br />
           &bull; Failed to connect to server. Error: 0x80070005
        </p>
    <p style="padding-left: 30px"><strong>Solution</strong>
        <p style="padding-left: 60px">
            &bull; The WMI service uses the Network Service account to access these resources, but the Network Service account does not have access to them.<br />
            &bull; Give the Network Service Read &amp; Execute permissions on the following folders...
            <p style="padding-left: 90px">
                &bull; C:Program FilesMicrosoft Office Servers14.0SQL<br />
                &bull; C:Program FilesMicrosoft Office Servers14.0Service<br />
                &bull; C:Program FilesMicrosoft Office Servers14.0Tools
            </p>
        </p>
    </p>

<strong>Event 6301</strong><br />
    <p style="padding-left: 30px"><strong>Error</strong>
        <p style="padding-left: 60px">
           BAIL: MMS(7824): eafam.cpp(1295): 0x80230304 (The image or dimage already has an attribute with that name.) 
BAIL: MMS(7824): eafam.cpp(943): 0x80230304 (The image or dimage already has an attribute with that name.) 
BAIL: MMS(7824): eafam.cpp(1010): 0x80230304 (The image or dimage already has an attribute with that name.) 
BAIL: MMS(7824): amexec.cpp(1630): 0x80230304 (The image or dimage already has an attribute with that name.) 
BAIL: MMS(7824): amexec.cpp(2018): 0x80230304 (The image or dimage already has an attribute with that name.) 
BAIL: MMS(7824): eaf.cpp(1373): 0x80230304 (The image or dimage already has an attribute with that name.) 
BAIL: MMS(7824): eaf.cpp(653): 0x80230304 (The image or dimage already has an attribute with that name.) 
ERR: MMS(7824): synccoreimp.cpp(5211): 0x80230304 - export-flow failed 0x80230304 
BAIL: MMS(7824): synccoreimp.cpp(5212): 0x80230304 (The image or dimage already has an attribute with that name.) 
BAIL: MMS(7824): synccoreimp.cpp(4816): 0x80230304 (The image or dimage already has an attribute with that name.) 
BAIL: MMS(7824): synccoreimp.cpp(10567): 0x80230304 (The image or dimage already has an attribute with that name.) 
BAIL: MMS(7824): synccoreimp.cpp(10313): 0x80230304 (The image or dimage already has an attribute with that name.) 
BAIL: MMS(7824): synccoreimp.cpp(2524): 0x80230304 (The image or dimage already has an attribute with that name.) 
BAIL: MMS(7824): synccoreimp.cpp(4333): 0x80230304 (The image or dimage already has an attribute with that name.) 
BAIL: MMS(7824): synccoreimp.cpp(8485): 0x80230304 (The image or dimage already has an attribute with that name.) 
BAIL: MMS(7824): synccoreimp.cpp(3802): 0x80230304 (The image or dimage already has an attribute with that name.) 
ERR: MMS(7824): synccoreimp.cpp(3818): 0x80230304 - CS to MV to CS synchronization failed 0x80230304: [CN=Doe\, John,OU=Contractors,OU=DE,DC=MYDOM,DC=com] 
BAIL: MMS(7824): synccoreimp.cpp(3623): 0x80230304 (The image or dimage already has an attribute with that name.) 
ERR: MMS(7824): syncmonitor.cpp(2512): SE: Rollback SQL transaction for: 0x80230304
        </p>
    </p>
    <p style="padding-left: 30px"><strong>Solution</strong>
        <p style="padding-left: 60px">
            This error occurs when you have 2 sources mapped to the same Profile Property<br />
            To fix, change the Policy for the property to 'Optional'. See <a href="http://blogs.technet.com/b/steve_chen/archive/2010/10/11/user-profile-import-from-bdc-fails-on-sharepoint-server-2010-with-event-id-6301.aspx">this blog post</a> for more info.<br />
            If that still doesn't work, then <a href="http://social.technet.microsoft.com/Forums/en-US/sharepoint2010setup/thread/f7e8e9fb-fa27-45fc-be15-70720a410d51/">this forum post</a> explains how to use the miisclient.exe to fix sync issues
        </p>
    </p>

<strong>MSDTC Error</strong><br />
    <p style="padding-left: 30px"><strong>Errors</strong>
        <p style="padding-left: 60px">
           &bull; System.Transactions.TransactionManagerCommunicationException: Network access for Distributed Transaction Manager (MSDTC) has been disabled. Please enable DTC for network access in the security configuration for MSDTC using the Component Services Administrative tool. —&gt; System.Runtime.InteropServices.COMException (0x8004D024): The transaction manager has disabled its support for remote/network transactions. (Exception from HRESULT: 0x8004D024)<br />
        </p>
    <p style="padding-left: 30px"><strong>Solution</strong>
        <p style="padding-left: 60px">
            &bull; Here is a <a href="http://discussion.accuwebhosting.com/windows-server/1251-network-access-distributed-transaction-manager-msdtc-has-been-disabled.html">blog post</a> that gives a step-by-step on how to resolve this.<br />
            &bull; Here are the basic steps on what to do.  Control Panel – Administrative Tools – Component Services – My Computer properties – MSDTC tab – Security Configuration tab – Network DTC Access (checked) / Allow Remote Clients (checked) / Allow Inbound (checked) / Allow Outbound (checked) / Enable TIP Transactions (checked)
        </p>
    </p>