Android lag issues in Galaxy S3? I know I have previously asked a similar question and I am asking again : why does my Galaxy S3 lag when doing routine tasks ?  


When pressing HOME button , the screen is supposed to smoothly fade away. Instead, it fades away in a stammering manner. Sometimes, it just stays and then disappears in an instant without the gradual fading effect. This was in case of Mozilla, Chrome and some other apps.  
The  drop down menu on the top of the screen also stammers when I open it. I do not drag my finger all the way to the bottom, I just click and flick and let the menu go down on its own. 


Is it a hardware issue ?
I do clear my cache once in a while. No task killer. No root.

As a side note, I play Real Racing quite often and I DO notice an occasional lag when there are like 20 cars driven together. Apart from that, game works like a charm.
With as advanced of a phone as the S3 is, you shouldn't be experiencing much, if any, lag at all. Chances are, it's something you have or haven't done to the phone. 
1. Try restarting it. Often times, RAM will remain in use even when applications are no longer being used. Restarting it will bring your phone back to where it's not using ram from all the apps you've been using since the last time you restarted it.
2. You said that you clear your cache... I'm assuming you mean RAM cache, versus data cache. Android's way of memory (RAM) cache "clearing" isn't always (or even often) entirely effective. An app I've fell in love with for cleaning out RAM (as well as it's anti-virus abilities) is 360 Mobile Security - Antivirus, which you can download from the app store. It'll force out memory in ways many apps don't, and also gives you the benefit of having an anti-virus program built in. Root gives more functionality to it, but you said you don't use root, but I thought I'd throw that out there for anyone reading this that might have root. 
3. Update your android system. 4.1.2 is not known for it's "buttery smooth interface and performance".   Settings -->  About phone --> Update (may be in status tab) will likely be able to update Android's platform for you. If not, outside of rooting and changing your rom, guess you'll be stuck with 4.1.2 unless your carrier provides an update service for you.
4. Check your settings. THere's things in the developer's options menu that'll effect transition speed, which can give appearances like lag.  Developers options --> window/transition animation scale  is the place you want to check. x1 seems to be a standard setting, but the lower you go, the faster the system will react visually, and (when available), I set mine to x.25, but that's not always an option (in ROMs), where-as x.5 usually is available. Use x.5 if x.25 isnt available. There's a couple other things in developer's options that could help you out too, take a look around.
5. Keep on researching the issue if this doesn't help. The answers are out there.