To start, there's the problem with the finger scanner. Apple thought that it would be a good idea to have a finger scanner on the home button. They thought that this was a good way to prevent theft and hacking into the system. Well, they thought wrong. People all over YouTube have posted videos of them hacking the finger scanner. After about 2 minutes they get passed the finger scanner and got into the data. They do this by taking a picture of the owner's finger off of the phone screen. They then take the picture, flip it, and reverse the facing of the photo. They then print the image onto a piece of latex and put it over their finger. They then can get into the owner's files and data.
Another problem is with the accelerometer. When comparing to the iPhone 5, the readings are different. You can also not play video games on the phone using the accelerometer because it doesn't read correctly.
Overall, people are disappointed with the iPhone 5s. Apple won't even acknowledge that there is an issue with the phone. The faster Apple does something about this, the faster the reputation of the iPhone stays good.