Off the top of my head my problems are:
Double tap doesn't work ever
Can't click install in playstore
GPS is useless
Copy and paste only works 1/2 the time
Can't paste number into text messages
Auto focus on videos is extremely slow
Trouble clicking into areas to bring up the keyboard occasionally
People complain my voice is quiet in phone calls
In general it's also sluggish
Battery life isn't horrible, but not as good as before.
Also my phone is an unbranded canadian version with no bloatware, or carrier programs installed. Supposedly the guy I bought it off of won it in a contest from lg or something along those lines. If I was to install a custom Rom would anyone have any idea which ones I can install without bricking my phone?