I have some issues with the G4, but I also have issues with every other Android phone available, and I have owned almost all of them at one point or another. The perfect phone for me simply does not exist as of now.
Issues with G4 (current daily driver):
-Touchscreen isn't very sensitive and occasionally misses taps. It doesn't happen very often for me, but it does happen. Hopefully this is improved with updates.
-Camera image processing sometimes applies too much noise reduction and / or sharpening.
-LG's software isn't as well designed as Google's, HTC's, or even Samsung's. Ugly colors, ugly icons, and less pretty animations. Thankfully Google provides most of their apps in the Play Store.
-Notifications sometimes can't be expanded without hiding the quick settings.
-Third party launchers don't perform that well on the G4. Google Now Launcher and Nova are mostly smooth, most of the time, but occasionally they start dropping frames and scrolling a little choppy, which doesn't happen on other phones.
-The chrome plastic on the sides of the phone is cheap feeling.
Issues with S6 (have owned it since launch, but about to sell it):
-The screen is too oversaturated in adaptive mode and too warm in basic mode. Also, it looks a little splotchy when displaying dark colors in dim light.
-Camera doesn't have good manual controls.
-Samsung's memory management forces apps out of memory way too quickly, meaning apps have to reload when switching back to them all the time.
-Scrolling performance in Chrome sucks.
-Meh battery life, especially in standby.
-Speaker is very high pitched and ear piercing at high volumes.
-Cell reception isn't great.
-Super slippery glass on the back means I had to put it in a case.
Issues with Nexus 6 (haven't owned it, but I know these things from playing with it):
-Screen is too oversaturated, and many are too warm.
-Camera is meh compared to the G4 and S6.
-Too big to use with one hand.
-Slippery back.
Issues with Note 4 (only owned this sucker for a couple days before returning it):
-The screen is too oversaturated in adaptive mode and too warm in basic mode.
-Camera isn't very good in low light compared to the G4 and S6.
-Camera doesn't have good manual controls.
-Laggier than the G4, S6, and Nexus 6. Can't handle it.
One M9 (Owned an M7 and M8, but not the M9. Can't deal with HTC's crappy cameras any more.):
-Worst camera of them all.
A G4 with better touch sensitivity, stock Android (except for LG Camera app), image processing from the S6, and metal sides instead of chrome plastic would be pretty baller.