I'm having the same problem; the updater starts and goes through the file check but crashes as soon as I click the "I Agree" button. The -renderthread 0 command parameter is added.
Here's the output when I save a log file:
** Mon Mar 21 15:16:12 2011
Starting '/home/eweb/cxgames/bin/wineloader' 'winewrapper.exe' '--workdir' '/home/eweb/.cxgames/CoH/dosdevices/c:/Program Files/City of Heroes' '--start' '--'
'/home/eweb/.cxgames/CoH/dosdevices/../drive_c/Program Files/City of Heroes/cohupdater.exe' '-renderthread' '0'
fixme:exec:SHELL_execute flags ignored: 0x00000100
fixme:shdocvw:PersistStorage_InitNew (0x136ab0)->(0x10112bb8)
fixme:urlmon:URLMoniker_BindToObject use running object table
fixme:system:SetProcessDPIAware stub!
fixme:winsock:WSAIoctl unsupported WS_IOCTL cmd (_WSAIOW(IOC_VENDOR, 300))
fixme:winsock:WSAIoctl unsupported WS_IOCTL cmd (_WSAIOW(IOC_VENDOR, 300))
fixme:iphlpapi:NotifyAddrChange (Handle 0xdfe914, overlapped 0xdfe918): stub
fixme:ntdll:NtLockFile I/O completion on lock not implemented yet
fixme:shdocvw:ClOleCommandTarget_QueryStatus (0x136b60)->((null) 1 0xaec204 (nil))
fixme:shdocvw:ClOleCommandTarget_QueryStatus command_0: 27, 0x0
fixme:shdocvw:ClOleCommandTarget_Exec Unimplemented cmdid 25
fixme:shdocvw:ClOleCommandTarget_Exec Unimplemented cmdid 26
fixme:shdocvw:ClOleCommandTarget_Exec Unimplemented group {000214d1-0000-0000-c000-000000000046}
fixme:shdocvw:ClientSite_GetContainer (0x136b60)->(0xaec1d4)
fixme:shdocvw:ClOleCommandTarget_Exec Unimplemented group {000214d1-0000-0000-c000-000000000046}
fixme:resource:GetGuiResources (0xffffffff,0): stub
This using a Vista bottle, Arch Linux, kernel 2.6.37.