Have you bought a new Galaxy S4? If you did, then it's very likely that you got irritated by the lag at least once, but probably more than once. Why is this a major problem? Because it's not something that just some faulty devices have, it's something that almost every unit has. Just take a look at any Galaxy S4 thread in the major forums, you'll see thousands of posts related to this issue. Why else is this a major problem? Because when you buy a $700 phone, which is supposed to be the best on the market, you DO NOT expect it to have lag.
Of course, the Galaxy S4 is packed with the fastest CPU and the newest software, but what good is that if it makes you insane when you see it stutters when you press the home button or when you enter an app. The problem is not the hardware of course, is the fact that Samsung didn't manage to get the best out of the processor, and now we have to wait for an update that fixes this.
The US carrier versions got some minor updates just a few days back. Some users say that it fixed the lag, some say it didn't. As I understand the performance has slightly improved but there are still lag issues overall.
Meanwhile, user MADDtec on YouTube was kind enough to share with us his solution to the Galaxy S4 lag. As you will see in the video, the lag is there and then it's not. But the solution rather optimizes visual effects and brings them to a minimum, so it's not that satisfactory to know that you cannot run everything at maximum performance without issues on a $700 device. Here's the video from MaDDtec: