Though the following workaround isn't technically sanctioned by Samsung, Google, or anyone else involved in the cutting of Local Search from your Galaxy S III, it'll certainly do the trick if you're willing to get your hands a little dirty. What we've got here is a situation in which Samsung appears to be pre-empting a move by Apple to sue their pants off with an axing of the functionality on their devices that Apple very well could catch them on - Local Search is its name, and appearing too similar to Siri is its game.
Now the developers at XDA have fixed up the situation real quick. What you'll have to do to "fix" your device is hacking - if that's not something you're in to, you're pretty much out of luck for the time being unless you want to try out an application like QuickDroid, of course. To hack and replace the functionality that Samsung has suddenly taken away this week, you'll have to do the following, per "eyecon82" at XDA Developers forum:
"NOTE: You need ROOT! and probably Root Explorer, so you can change permissions, I did it all through the phone, I'm sure you could also use adb but this seemed simpler. Also, I don't think this can in any way break your phone, but just to be safe, make a backup, at least in Titanium, and don't blame me if something goes wrong.
1) Download the apk at the beginning of this thread, place it on your SDcard (or phone) where you'll find it easily.
2) Install root explorer (or equivalent, I used root explorer though)
3) Go to /system/app and mount as R/W
4) move GoogleQuickSearch.apk somewhere else, just so you have it if you need to restore it
5) Go to where you placed the full-featured apk, copy/move it to /system/app
6) Long-Click on GoogleQuickSearch.apk, select permissions, and set to rw-r--r-- (ie, row 1: yes yes no, row 2: yes no no, row 3: yes no no)
7) Hit okay, mount R/O, and quit
8) Go to Settings > Application Manager > All
9) Select Google Search, and clear data/cache
10) Select Google Services Framework, clear data/cache
13) Profit!!!" - eyecon82
At the moment this fix only works with one of several of the versions of the device, but we're expecting files to function for all models in the very near future. Have a peek at [the original XDA thread] to grab the APK you'll need to make Local Search work once again - and good luck!
Of course, as with all hacking adventures, we must inform you that whatever you do, you are responsible for your own actions. Doing any or all of the above could and likely will result in your device's warrantee to be stoppered and your brain to melt - so beware!