[Nexus S Q&A, Help & Troubleshooting] Hyperbo:
I was on a business trip and could try it just today. I didn't find a helium log file, so I looked at the link in your signature. I used the adb logcat variant. Here are my results:

Helium Version: 1.1.2.1 (not premium)

After starting the adb log on the console I backuped the SMS and it worked as expected. Then I tried an app for which the backup failed in the past (gnucash), but strangely it went through. I tried it again and it failed. I tried other apps, but couldn't reproduce the success. I chose the gnucash app because with the normal "adb backup -f ..." call it works just fine, so helium shouldn't have any problems.

Here is the log of one of the tries. First the successful SMS backup then the failed gnucash backup:

I/Carbon (14917): startBackup invoked: file
I/Carbon (14917): com.android.providers.telephony
D/PhoneStatusBar( 354): addNotification score=0
I/Carbon (14917): Releasing locks.
I/Carbon (14917): Acquiring full lock.
I/CarbonNonce(14917): Nonce: 9352e3b8-6553-4b27-a014-96283d88a017
I/Carbon (14917): bu 1 backup
D/SizeAdaptiveLayout( 354): com.android.internal.widget.SizeAdaptiveLayout@41a12ae0child view android.widget.FrameLayout@416316a0 measured out of bounds at 95px clamped to 96px
D/dalvikvm(14917): GC_FOR_ALLOC freed 963K, 13% free 13649K/15559K, paused 157ms, total 161ms
I/Carbon (14917): Demux atomic: false
D/dalvikvm(14917): GC_FOR_ALLOC freed 806K, 15% free 13363K/15559K, paused 68ms, total 69ms
I/Carbon (14917): Writing package: com.android.providers.telephony
I/CarbonBackup(14917): Package: com.android.providers.telephony
D/SizeAdaptiveLayout( 354): com.android.internal.widget.SizeAdaptiveLayout@41a12ae0child view android.widget.FrameLayout@416316a0 measured out of bounds at 95px clamped to 96px
D/dalvikvm(14917): GC_CONCURRENT freed 1606K, 13% free 13544K/15559K, paused 22ms+12ms, total 115ms
D/dalvikvm(14917): WAIT_FOR_CONCURRENT_GC blocked 44ms
D/dalvikvm(14917): GC_CONCURRENT freed 1849K, 13% free 13544K/15559K, paused 21ms+7ms, total 93ms
D/dalvikvm(14917): WAIT_FOR_CONCURRENT_GC blocked 30ms
D/dalvikvm(14917): GC_CONCURRENT freed 1848K, 13% free 13543K/15559K, paused 20ms+8ms, total 101ms
D/dalvikvm(14917): WAIT_FOR_CONCURRENT_GC blocked 43ms
D/dalvikvm(14917): GC_CONCURRENT freed 1847K, 13% free 13543K/15559K, paused 18ms+10ms, total 109ms
D/dalvikvm(14917): WAIT_FOR_CONCURRENT_GC blocked 55ms
D/dalvikvm(16484): GC_CONCURRENT freed 445K, 6% free 9865K/10439K, paused 12ms+3ms, total 1067ms
I/ActivityManager( 247): Start proc android.process.acore for content provider com.android.providers.contacts/.CallLogProvider: pid=16516 uid=10007 gids={3003, 1015, 1028}
I/ActivityThread(16516): Pub call_log: com.android.providers.contacts.CallLogProvider
I/ActivityThread(16516): Pub com.android.voicemail: com.android.providers.contacts.VoicemailContentProvider
I/ActivityThread(16516): Pub user_dictionary: com.android.providers.userdictionary.UserDictionaryProvider
I/ActivityManager( 247): Process com.android.backupconfirm (pid 16090) has died.
I/ActivityThread(16516): Pub applications: com.android.providers.applications.ApplicationsProvider
I/ActivityThread(16516): Pub contacts;com.android.contacts: com.android.providers.contacts.ContactsProvider2
D/dalvikvm(16516): GC_CONCURRENT freed 233K, 5% free 8230K/8583K, paused 82ms+15ms, total 135ms
D/dalvikvm(14917): GC_CONCURRENT freed 1831K, 13% free 13561K/15559K, paused 15ms+5ms, total 101ms
D/dalvikvm(14917): WAIT_FOR_CONCURRENT_GC blocked 36ms
D/dalvikvm(14917): GC_FOR_ALLOC freed 390K, 14% free 13501K/15559K, paused 53ms, total 54ms
D/dalvikvm(14917): GC_FOR_ALLOC freed 2K, 12% free 13755K/15559K, paused 42ms, total 42ms
I/CarbonParser(14917): Finished demuxing com.android.providers.telephony
I/Carbon (14917): Completed: com.android.providers.telephony
I/Carbon (14917): Releasing locks.
I/Carbon (14917): Stopping.
W/InputMethodManagerService( 247): Window already focused, ignoring focus gain of: com.android.internal.view.IInputMethodClient$Stub$Proxy@41f8f688 attribute=android.view.inputmethod.EditorInfo@41f71d70
D/dalvikvm(16516): GC_CONCURRENT freed 51K, 3% free 8593K/8775K, paused 45ms+5ms, total 130ms
D/dalvikvm(16484): GC_CONCURRENT freed 361K, 5% free 10040K/10503K, paused 39ms+49ms, total 566ms
D/dalvikvm(14917): GC_FOR_ALLOC freed 769K, 13% free 13796K/15751K, paused 162ms, total 164ms
I/ExternalStorage(14917): main: /storage/sdcard0
I/ExternalStorage(14917): other main: /storage/sdcard0
I/ExternalStorage(14917): Vol: /storage/sdcard0
I/ExternalStorage(14917): vols in list: 0
I/ActivityManager( 247): Process com.google.android.apps.plus (pid 16214) has died.
D/dalvikvm(16484): GC_CONCURRENT freed 492K, 6% free 10152K/10759K, paused 43ms+15ms, total 152ms
I/Carbon (14917): startBackup invoked: file
I/Carbon (14917): org.gnucash.android
D/PhoneStatusBar( 354): addNotification score=0
I/Carbon (14917): Releasing locks.
I/Carbon (14917): Acquiring full lock.
I/CarbonNonce(14917): Nonce: 36bea2ce-0ba5-4f0e-88d2-650fea91196b
I/Carbon (14917): bu 1 backup org.gnucash.android
W/System.err(14917): java.io.IOException: Connection refused
D/SizeAdaptiveLayout( 354): com.android.internal.widget.SizeAdaptiveLayout@419f7df8child view android.widget.FrameLayout@41986318 measured out of bounds at 95px clamped to 96px
W/System.err(14917): at android.net.LocalSocketImpl.connectLocal(Native Method)
W/System.err(14917): at android.net.LocalSocketImpl.connect(LocalSocketImpl.java:238)
W/System.err(14917): at android.net.LocalSocket.connect(LocalSocket.java:98)
W/System.err(14917): at com.koushikdutta.shellproxy.ShellProcess2.<init>(ShellProcess2.java:124)
W/System.err(14917): at com.koushikdutta.shellproxy.ShellProcess2.exec(ShellProcess2.java:30)
W/System.err(14917): at com.koushikdutta.backup.BackupServiceHelper$11.onContinue(BackupServiceHelper.java:735)
W/System.err(14917): at com.koushikdutta.async.future.Continuation.next(Continuation.java:119)
W/System.err(14917): at com.koushikdutta.async.future.Continuation.start(Continuation.java:154)
W/System.err(14917): at com.koushikdutta.backup.BackupRestoreService$1$4.run(BackupRestoreService.java:246)
I/Carbon (14917): Releasing locks.
I/Carbon (14917): Stopping.
I/System.out(14917): Connection refused
E/ActivityThread(14917): Service com.koushikdutta.backup.BackupRestoreService has leaked ServiceConnection android.media.MediaScannerConnection@417ebfc8 that was originally bound here
E/ActivityThread(14917): android.app.ServiceConnectionLeaked: Service com.koushikdutta.backup.BackupRestoreService has leaked ServiceConnection android.media.MediaScannerConnection@417ebfc8 that was originally bound here
E/ActivityThread(14917): at android.app.LoadedApk$ServiceDispatcher.<init>(LoadedApk.java:965)
E/ActivityThread(14917): at android.app.LoadedApk.getServiceDispatcher(LoadedApk.java:859)
E/ActivityThread(14917): at android.app.ContextImpl.bindService(ContextImpl.java:1191)
E/ActivityThread(14917): at android.app.ContextImpl.bindService(ContextImpl.java:1183)
E/ActivityThread(14917): at android.content.ContextWrapper.bindService(ContextWrapper.java:394)
E/ActivityThread(14917): at android.media.MediaScannerConnection.connect(MediaScannerConnection.java:116)
E/ActivityThread(14917): at com.koushikdutta.backup.data.FileBackupPackage.<init>(FileBackupPackage.java:34)
E/ActivityThread(14917): at com.koushikdutta.backup.BackupRestoreService$1.startBackup(BackupRestoreService.java:128)
E/ActivityThread(14917): at com.koushikdutta.backup.BackupFragment$11.onServiceConnected(BackupFragment.java:340)
E/ActivityThread(14917): at android.app.LoadedApk$ServiceDispatcher.doConnected(LoadedApk.java:1097)
E/ActivityThread(14917): at android.app.LoadedApk$ServiceDispatcher$RunConnection.run(LoadedApk.java:1114)
E/ActivityThread(14917): at android.os.Handler.handleCallback(Handler.java:615)
E/ActivityThread(14917): at android.os.Handler.dispatchMessage(Handler.java:92)
E/ActivityThread(14917): at android.os.Looper.loop(Looper.java:137)
E/ActivityThread(14917): at android.app.ActivityThread.main(ActivityThread.java:4745)
E/ActivityThread(14917): at java.lang.reflect.Method.invokeNative(Native Method)
E/ActivityThread(14917): at java.lang.reflect.Method.invoke(Method.java:511)
E/ActivityThread(14917): at com.android.internal.os.ZygoteInit$MethodAndArgsCaller.run(ZygoteInit.java:786)
E/ActivityThread(14917): at com.android.internal.os.ZygoteInit.main(ZygoteInit.java:553)
E/ActivityThread(14917): at dalvik.system.NativeStart.main(Native Method)
D/dalvikvm(16484): GC_CONCURRENT freed 554K, 7% free 10213K/10887K, paused 22ms+16ms, total 128ms
I/Ads (14917): Ad is not visible. Not refreshing ad.
I/Ads (14917): Scheduling ad refresh 60000 milliseconds from now.
W/InputMethodManagerService( 247): Window already focused, ignoring focus gain of: com.android.internal.view.IInputMethodClient$Stub$Proxy@42291968 attribute=null
D/dalvikvm( 247): GC_CONCURRENT freed 1764K, 18% free 22183K/26887K, paused 17ms+12ms, total 234ms