Finder Search (spotlight) not finding all relevant results

The Spotlight window does not include files treated as system files by default. Try setting "System files" to "are included":

Or use mdfind:

$ mdfind -name tweetbot
/Applications/Tweetbot.app
/Users/lauri/Library/Application Support/CrashReporter/Tweetbot_4C49445B-E14E-51E5-87DC-7CE59AE6A841.plist
/Users/lauri/Library/Containers/com.tapbots.TweetbotMac/Data/Library/Application Support/CrashReporter/Tweetbot_4C49445B-E14E-51E5-87DC-7CE59AE6A841.plist
/Users/lauri/Library/Containers/com.tapbots.TweetbotMac/Data/Library/Application Support/Tweetbot
/Users/lauri/Library/Containers/com.tapbots.TweetbotMac
/Users/lauri/Library/Speech/Speakable Items/Application Speakable Items/Tweetbot
/Users/lauri/Library/SyncedPreferences/com.tapbots.TweetbotMac.plist