Who I have the same questioned this topic

Hi all.  I just got my note 3 last week Monday.   I've been noticing some charging issues.   Using the rapid charger that came with my device....if I turn my phone OFF and leave it to charge over night it will only be at 99% in the morning when I turn it on.  It quickly goes to 98 or 97 within a minute and I haven't even had time to check my emails!   Now IF I leave the phone on I can get it to charge to 100%?   Odd??  Also sometimes when I plug the charger in it won't start charging right away until I give it a wiggle.  I spoke to Verizon rep who is sending me a new battery.  I will see if that makes a difference, but I would prefer to not have to go exchange for a new device if I don't have to because I just had a nice tempered glass anti fingerprint screen protector put on.  Has anyone here experienced any of this?  Thanks!!