You'll notice tuning problems mainly because the strings slip at the nut. This is why guitars with a floyd rose have locking nuts. You'll see people go nuts on the whammy bar and be able to stay in tune because since the string is locked into place it stays the same (assuming the strings were stretched previously). After the nut is the string tree (if your guitar hes them). Finally the actual tuning post. Your string can slip slightly in any of these areas and can send your guitar sharp/flat in an instant.
What kind of music do you play and what exactly do you want to use the whammy bar for? Slight vibrato or heavy use of the bar like for heavy metal stuff?