This is the log output that appears when I get the error popup:

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[DEBUG 15:54:02.537] BackgroundSyncChecker: Detected that sync would be a good idea now
[DEBUG 15:54:02.644] SyncThread using SyncServiceAddin: Tomboy Web
[DEBUG 15:54:02.644] SilentUI: SyncStateChanged: Connecting
[DEBUG 15:54:02.923] SilentUI: SyncStateChanged: AcquiringLock
[DEBUG 15:54:02.923] Building web request for URL: https://one.ubuntu.com/notes/api/1.0/
[DEBUG 15:54:03.355] Building web request for URL: https://one.ubuntu.com/notes/api/1.0/user/
[DEBUG 15:54:04.541] 8
[DEBUG 15:54:04.541] SilentUI: SyncStateChanged: PrepareDownload
[DEBUG 15:54:04.541] Sync: GetNoteUpdatesSince rev 760
[DEBUG 15:54:04.541] Building web request for URL: https://one.ubuntu.com/notes/api/1.0/op/?include_notes=true&since=760
[DEBUG 15:54:05.806] Sync: 0 updates since rev 760
[DEBUG 15:54:05.807] Building web request for URL: https://one.ubuntu.com/notes/api/1.0/op/
[DEBUG 15:54:07.994] SilentUI: SyncStateChanged: PrepareUpload
[DEBUG 15:54:07.995] Saving 'Notes Clean Up'...
[DEBUG 15:54:07.995] Saving 'Notes Clean Up'...
[DEBUG 15:54:08.522] SilentUI: NoteSynchronized, Title: Notes Clean Up, Type: UploadModified
[DEBUG 15:54:08.523] Sync: Uploading 1 note updates
[DEBUG 15:54:08.523] SilentUI: SyncStateChanged: Uploading
[DEBUG 15:54:08.544] Building web request for URL: https://one.ubuntu.com/notes/api/1.0/op/
[ERROR 15:54:08.677] Exception while saving note: System.IO.IOException: Sharing violation on path /home/andreas/.local/share/tomboy/965900ba-ab15-4e67-8c8e-64b86e9fa9da.note.tmp
  at System.IO.FileStream..ctor (System.String path, FileMode mode, FileAccess access, FileShare share, Int32 bufferSize, Boolean anonymous, FileOptions options) [0x00000] in <filename unknown>:0 
  at System.IO.FileStream..ctor (System.String path, FileMode mode, FileAccess access, FileShare share) [0x00000] in <filename unknown>:0 
  at (wrapper remoting-invoke-with-check) System.IO.FileStream:.ctor (string,System.IO.FileMode,System.IO.FileAccess,System.IO.FileShare)
  at System.IO.StreamWriter..ctor (System.String path, Boolean append, System.Text.Encoding encoding, Int32 bufferSize) [0x00000] in <filename unknown>:0 
  at System.IO.StreamWriter..ctor (System.String path, Boolean append, System.Text.Encoding encoding) [0x00000] in <filename unknown>:0 
  at (wrapper remoting-invoke-with-check) System.IO.StreamWriter:.ctor (string,bool,System.Text.Encoding)
  at System.Xml.XmlWriter.Create (System.String file, System.Xml.XmlWriterSettings settings) [0x00000] in <filename unknown>:0 
  at Tomboy.NoteArchiver.WriteFile (System.String write_file, Tomboy.NoteData note) [0x00000] in <filename unknown>:0 
  at Tomboy.NoteArchiver.Write (System.String write_file, Tomboy.NoteData note) [0x00000] in <filename unknown>:0 
  at Tomboy.Note.Save () [0x00000] in <filename unknown>:0 
[DEBUG 15:54:09.262] Saving 'Ubuntu Oneiric Ocelot: Post-install'...
[DEBUG 15:54:12.093] SilentUI: SyncStateChanged: CommittingChanges
[DEBUG 15:54:12.093] Building web request for URL: https://one.ubuntu.com/notes/api/1.0/op/
[DEBUG 15:54:14.269] SilentUI: SyncStateChanged: Succeeded
[DEBUG 15:54:14.426] Sync: New revision: 761
[DEBUG 15:54:14.427] SilentUI: SyncStateChanged: Idle