Problem:

Preview crashes upon launch due to a sandbox error.

Solution

Create the missing "Containers" folder in ~/Library/ by running this command in the terminal.

mkdir ~/Library/Containers

Crash Report

Process:         Preview
Path:            /Applications/Preview.app/Contents/MacOS/Preview
Identifier:      com.apple.Preview
Version:         5.5 (719)
Build Info:      Preview-719000000000000~1
Code Type:       X86-64 (Native)
Parent Process:  launchd

OS Version:      Mac OS X 10.7 (11A511)
Report Version:  9

Crashed Thread:  0  Dispatch queue: com.apple.main-thread

Exception Type:  EXC_BAD_INSTRUCTION (SIGILL)
Exception Codes: 0x0000000000000001, 0x0000000000000000

Application Specific Information:
dyld: launch, running initializers
/usr/lib/libSystem.B.dylib
xpchelper reply message validation: sandbox creation failed: 1002
Container object initialization failed: NSCocoaErrorDomain:513 You don’t have permission to save the file “Containers” in the folder “Library”.
 
Dest: ~/Library/Containers/com.apple.Preview/Data/Library/Preferences
Destination permissions info:
  0 stat: 2
 -1 stat: 2
 -2 stat: 2
 -3 stat: 2
 -4 stat: 2
 -5 m:040775 R acl:(null) LIBRARY
    fs: hfs, fsid: e000002, mf: 0480d000
 -6 m:040775 R acl:(null) HOME
    fs: hfs, fsid: e000002, mf: 0480d000
 -7 m:040755 R acl:(null)
    fs: hfs, fsid: e000002, mf: 0480d000

Application Specific Signatures:
sandbox creation failed: 1002