I've uploaded Data Object Manager but when I try to build my database I get a host of errors:

Strict Standards: Declaration of DataObjectManager::FieldHolder() should be compatible with that of ComplexTableField::FieldHolder() in host/silverstripe3/dataobject_manager/code/DataObjectManager.php on line 4

Strict Standards: Declaration of DataObjectManager_Item::Link() should be compatible with that of ComplexTableField_Item::Link() in host/silverstripe3/dataobject_manager/code/DataObjectManager.php on line 648

Strict Standards: Declaration of DataObjectManager_Item::Fields() should be compatible with that of TableListField_Item::Fields() in host/silverstripe3/dataobject_manager/code/DataObjectManager.php on line 648

Strict Standards: Declaration of DataObjectManager_ItemRequest::Link() should be compatible with that of ComplexTableField_ItemRequest::Link() in host/silverstripe3/dataobject_manager/code/DataObjectManager.php on line 919

Strict Standards: Declaration of AssetManagerFolder::updateCMSFields() should be compatible with that of DataExtension::updateCMSFields() in host/silverstripe3/dataobject_manager/code/AssetManagerFolder.php on line 4

Fatal error: Class 'SortableDataObject' not found in host/silverstripe3/dataobject_manager/code/DataObjectManager.php on line 64

Any idea where I've gone wrong?

DOM is no longer compatible/recommend for use in SS3.0. I think UncleCheese may have updated it to work in 3 (check github) but otherwise you should now be using gridField instead of DOM for your relationship management.

Fantastic, thanks!