Problems? That sucks! Sorry to hear. If your Motorola Moto G needs a little TLC, you have a couple options. You could contact the store where you originally purchased the device or you could contact Motorola directly. Your eligibility for repair, replacement or support may depend on the warranty period remaining. Good luck!
Safe mode starts the device without any 3rd party applications being started. This will allow you to open apps individually to try and determine which app may be causing the issue.
Simply restart your phone, it should get out of safe mode.
Let me know if you're out of safe mode.