The info I am including below is how to turn it off. However, none of it will work, or work permanently, until you get the button fixed.
To get out of Safe Mode, please try the following.
1. Touch and Hold the "Power" key.
2. Tap "Power Off".
3. Once the phone is off, Touch and Hold the "Power" key again to restart.
The phone should now be out of "Safe Mode".
If the "Safe Mode" is still running after you restart your phone, I would then check to make sure your "Volume Down" button is not stuck. Check to see if it has anything stuck in it as well, dust, etc. Anything like this can cause the phone to go into, and get stuck in, "Safe Mode".
If that doesn't work try this...
Use the "Status Bar" to turn off "Safe Mode'. Pull down (swipe) the "Status Bar" of your phone. Now tap the "Safe Mode" button. This should turn "Safe Mode" off. Now your phone will automatically restart, so that it boots up out of "Safe Mode".
If you want to get rid of/disable "Safe Mode".
1. First turn off the phone.
2. Next press and hold "Power" until you see the manufacturers logo on the screen, then release the power button.
3. "Quickly" press "Volume Down" and hold it for few seconds until you see the message "Safe Mode: OFF" or something similar.
4. If you wanted re-enable it, simply repeat the steps above, and you should see "Safe mode: ON" rather than off.
If you are trying to do a factory restore on it, you can do it from inside Android through settings. If you can't get to that, you need to fix the button, or try flashing the factory ROM using a computer, but that method may also need you to get into a service mode.