In my case, I had the same error with the text at the end of this entry in the logs. However, the cause revealed by procmon.exe was that c:\windows\syswow64\msvcr71.dll could not be overwritten (Write File). Seems reasonable, but that seems to be a standard corrective action by the VMWare code when it can't read msvcr71.dll. Somehow the local users had no read access to the file msvcr71.dll. After giving them read access, a non-admin user can connect to a central vmware cluster.
[ :startup :W: 1] 2015-03-02 21:33:33.398 Log for vSphere Client Launcher, pid=16256, version=5.1.0, build=build-1064113, option=release
[ :Error :W: 1] 2015-03-02 21:33:33.436 System.UnauthorizedAccessException: Attempted to perform an unauthorized operation.
at Microsoft.Win32.RegistryKey.Win32Error(Int32 errorCode, String str)
at Microsoft.Win32.RegistryKey.SetValue(String name, Object value, RegistryValueKind valueKind)
at Microsoft.Win32.RegistryKey.SetValue(String name, Object value)
at VpxClient.Program.RegisterClientMimeExtension()
[ :QuickInf:W: 6] 2015-03-02 21:33:38.656 Set the dll search path to C:\Program Files (x86)\VMware\Infrastructure\Virtual Infrastructure Client\5.1
[ :QuickInf:W: 6] 2015-03-02 21:33:38.800 Load Shared DLLs: C:\Program Files (x86)\VMware\Infrastructure\Virtual Infrastructure Client\5.1
[ :startup :W: 6] 2015-03-02 21:33:39.349 Log for vSphere Client, pid=16256, version=5.1.0, build=build-1064113, option=release, user=root, url = https://ws156/sdk
[ :ShowExcp:W: 6] 2015-03-02 21:33:40.148 Error: Could not load file or assembly 'VpxClient.SSPI, Version=2.0.14.0, Culture=neutral, PublicKeyToken=9f0928b6ea506bde' or one of its dependencies. Access is denied.
System.IO.FileLoadException: Could not load file or assembly 'VpxClient.SSPI, Version=2.0.14.0, Culture=neutral, PublicKeyToken=9f0928b6ea506bde' or one of its dependencies. Access is denied.
at VmomiSupport.ServiceManager.NewLoginSpec()
at VMware.Vim.Client.VimClient.GetAnonymousLoginSpec(Dictionary`2 specMap)
at VpxClient.UI.InitializeVimClient(Dictionary`2 specMap, String[] arguments)
at VpxClient.UI.StartUpIfNotMultiVcSecure(Dictionary`2 specMap, SecureString password, String[] arguments, LoginEventHandler handler, String dllPath, List`1 listOfVcUrls)
System.UnauthorizedAccessException: Access is denied. (Exception from HRESULT: 0x80070005 (E_ACCESSDENIED))
--- End of inner exception stack trace ---