I managed to get my data back by reinstalling Snow Leopard an using the Migration Assistant. However, it seems the backup I did just before erasing the drive wasn't saved. Or maybe the one time I successfully restored (with error messages, but it worked at least) it deleted the latest backup just because I restored from the second latest backup instead. Looking through the backup drive, it seems the data is indeed lost, but at least I got most of it back.
I'd love to know why it didn't work, but maybe I shouldn't care but just ditch Time Machine. It seems like it's just a false sense of security. Is Carbon Copy Cloner really the way to go?
If anyone is interested, here is the (as far as I can see) relevant part of the log:
EDIT: Is there no better way to post logs? It's impossible to read!
Jun 19 06:16:47 localhost OSInstaller[154]: [RESTORE] restoring from: /Volumes/LaCie/Backups.backupdb/Johan SwetzeÃÅns MacBook Pro/2011-06-18-002034/Macintosh HD
Jun 19 06:16:47 localhost OSInstaller[154]: [RESTORE] restoring to: /Volumes/Macintosh HD
Jun 19 06:16:47 localhost OSInstaller[154]: [RESTORE] filelist: (\n ".DS_Store",\n ".file",\n ".vbt5",\n ".vol",\n "Anva\U0308ndarhandbo\U0308cker och information",\n Applications,\n bin,\n cores,\n Developer,\n etc,\n imageout,\n "Incompatible Software",\n Library,\n "lost+found",\n "mach_kernel",\n Network,\n opt,\n sbin,\n System,\n tmp,\n "tmp.3jLDGt",\n "tmp.3jLDGt.meta",\n "tmp.738HCU",\n "tmp.738HCU.meta",\n "tmp.BPQfwE",\n "tmp.BPQfwE.meta",\n "tmp.BvLcpj",\n "tmp.BvLcpj.meta",\n "tmp.hHW90u",\n "tmp.hHW90u.meta",\n "tmp.hpmksm",\n "tmp.hpmksm.meta",\n "tmp.IA0gAl",\n "tmp.IA0gAl.meta",\n "tmp.iCgAhv",\n "tmp.iCgAhv.meta",\n "tmp.k2xOHl",\n "tmp.k2xOHl.meta",\n "tmp.kWBZr0",\n "tmp.kWBZr0.meta",\n "tmp.KXMAGr",\n "tmp.KXMAGr.meta",\n "tmp.mlbpTh",\n "tmp.mlbpTh.meta",\n "tmp.mrpnCY",\n "tmp.mrpnCY.meta",\n "tmp.p5cfcC",\n "tmp.p5cfcC.meta",\n "tmp.qEJHpM",\n "tmp.qEJHpM.meta",\n "tmp.qV0rad",\n "tmp.qV0rad.meta",\n "tmp.S0NAW3",\n "tmp.S0NAW3.meta",\n "tmp.S0rcMA",\n "tmp.S0rcMA.meta",\n "tmp.TGjgGM",\n "tmp.TGjgGM.meta",\n "tmp.UExGFz",\n "tmp.UExGFz.meta",\n "tmp.vGOV1M",\n "tmp.vGOV1M.meta",\n "tmp.VPaApw",\n "tmp.VPaApw.meta",\n Users,\n usr,\n var,\n Volumes,\n "xbmc.log",\n "xbmc.old.log",\n "private/etc",\n "private/tftpboot",\n "private/tmp",\n "private/var"\n)
Jun 19 06:16:47 localhost OSInstaller[154]: Constructing critical restore paths
Jun 19 06:16:47 localhost OSInstaller[154]: [RESTORE] 1: restoring .DS_Store
Jun 19 06:16:47 localhost OSInstaller[154]: from source path: /Volumes/LaCie/Backups.backupdb/Johan SwetzeÃÅns MacBook Pro/2011-06-18-002034/Macintosh HD/.DS_Store
Jun 19 06:16:47 localhost OSInstaller[154]: to destination path: /Volumes/Macintosh HD
Jun 19 06:16:47 localhost OSInstaller[154]: [RESTORE] 2: restoring .file
Jun 19 06:16:47 localhost OSInstaller[154]: from source path: /Volumes/LaCie/Backups.backupdb/Johan SwetzeÃÅns MacBook Pro/2011-06-18-002034/Macintosh HD/.file
Jun 19 06:16:47 localhost OSInstaller[154]: to destination path: /Volumes/Macintosh HD
Jun 19 06:16:47 localhost OSInstaller[154]: [RESTORE] 3: restoring .vbt5
Jun 19 06:16:47 localhost OSInstaller[154]: from source path: /Volumes/LaCie/Backups.backupdb/Johan SwetzeÃÅns MacBook Pro/2011-06-18-002034/Macintosh HD/.vbt5
Jun 19 06:16:47 localhost OSInstaller[154]: to destination path: /Volumes/Macintosh HD
Jun 19 06:16:47 localhost OSInstaller[154]: [RESTORE] 4: restoring .vol
Jun 19 06:16:47 localhost OSInstaller[154]: from source path: /Volumes/LaCie/Backups.backupdb/Johan SwetzeÃÅns MacBook Pro/2011-06-18-002034/Macintosh HD/.vol
Jun 19 06:16:47 localhost OSInstaller[154]: to destination path: /Volumes/Macintosh HD
Jun 19 06:16:47 localhost OSInstaller[154]: [RESTORE] 5: restoring AnvaÃàndarhandboÃàcker och information
Jun 19 06:16:47 localhost OSInstaller[154]: from source path: /Volumes/LaCie/Backups.backupdb/Johan SwetzeÃÅns MacBook Pro/2011-06-18-002034/Macintosh HD/AnvaÃàndarhandboÃàcker och information
Jun 19 06:16:47 localhost OSInstaller[154]: to destination path: /Volumes/Macintosh HD
Jun 19 06:16:47 localhost OSInstaller[154]: [RESTORE] 6: restoring Applications
Jun 19 06:16:47 localhost OSInstaller[154]: from source path: /Volumes/LaCie/Backups.backupdb/Johan SwetzeÃÅns MacBook Pro/2011-06-18-002034/Macintosh HD/Applications
Jun 19 06:16:47 localhost OSInstaller[154]: to destination path: /Volumes/Macintosh HD
Jun 19 06:20:02 localhost OSInstaller[154]: [RESTORE] Error -22 while restoring /Volumes/LaCie/Backups.backupdb/Johan SwetzeÃÅns MacBook Pro/2011-06-18-002034/Macintosh HD/Applications/Adobe Flash CS4/en/Configuration/Libraries/Sounds.fla to (null)
Jun 19 06:33:22 localhost OSInstaller[154]: [RESTORE] Error -22 while restoring /Volumes/LaCie/Backups.backupdb/Johan SwetzeÃÅns MacBook Pro/2011-06-18-002034/Macintosh HD/Applications/The Sims 3.localized/The Sims3.app/Contents/Resources/transgaming/c_drive/Program Files/Electronic Arts/The Sims 3/Caches/Sunset Valley.objectCache to (null)
Jun 19 06:33:46 localhost OSInstaller[154]: [RESTORE] Error -22 while restoring /Volumes/LaCie/Backups.backupdb/Johan SwetzeÃÅns MacBook Pro/2011-06-18-002034/Macintosh HD/Applications/The Sims 3.localized/The Sims3.app/Contents/Resources/transgaming/c_drive/Program Files/Electronic Arts/The Sims 3/GameData/Shared/Packages/FullBuild1.package to (null)
Jun 19 06:33:47 localhost OSInstaller[154]: [RESTORE] Error -22 while restoring /Volumes/LaCie/Backups.backupdb/Johan SwetzeÃÅns MacBook Pro/2011-06-18-002034/Macintosh HD/Applications/The Sims 3.localized/The Sims3.app/Contents/Resources/transgaming/c_drive/Program Files/Electronic Arts/The Sims 3/GameData/Shared/Packages/FullBuild2.package to (null)
Jun 19 06:35:15 localhost LCA[79]: Child exited with status 11
Jun 19 06:35:18 localhost Unknown[270]: Launching the Installer Crash Log Viewer
Jun 19 06:35:52 localhost ReportCrash[268]: Process: Mac OS X Installer [154]
Jun 19 06:35:52 localhost ReportCrash[268]: Path: /System/Installation/CDIS/Mac OS X Installer.app/Contents/MacOS/Mac OS X Installer
Jun 19 06:35:53 localhost ReportCrash[268]: Identifier: Mac OS X Installer
Jun 19 06:35:53 localhost ReportCrash[268]: Version: ??? (???)
Jun 19 06:35:53 localhost ReportCrash[268]: Code Type: X86-64 (Native)
Jun 19 06:35:53 localhost ReportCrash[268]: Parent Process: LCA [79]
Jun 19 06:35:53 localhost ReportCrash[268]:
Jun 19 06:35:53 localhost ReportCrash[268]: Date/Time: 2011-06-19 06:34:50.242 -0700
Jun 19 06:35:53 localhost ReportCrash[268]: OS Version: Mac OS X 10.6 (10A432)
Jun 19 06:35:53 localhost ReportCrash[268]: Report Version: 6
Jun 19 06:35:53 localhost ReportCrash[268]:
Jun 19 06:35:53 localhost ReportCrash[268]: Exception Type: EXC_BAD_ACCESS (SIGSEGV)
Jun 19 06:35:53 localhost ReportCrash[268]: Exception Codes: KERN_INVALID_ADDRESS at 0x0000000000000011
Jun 19 06:35:53 localhost ReportCrash[268]: Crashed Thread: 0 Dispatch queue: com.apple.main-thread
Jun 19 06:35:53 localhost ReportCrash[268]:
Jun 19 06:35:53 localhost ReportCrash[268]: Application Specific Information:
Jun 19 06:35:53 localhost ReportCrash[268]: objc_msgSend() selector name: release
Jun 19 06:35:53 localhost ReportCrash[268]: