I've not had charging issues with the 610 over a year a half and two watches, but I did exchange my first one due to the strap pins falling out (didn't become a problem until nearly a year of use).
The main problem with my 610 relates to going out of range of the computer when the watch is transferring activities. Since it does this automatically, and my computer is often on, this happens occassionally when I am unaware that the watch is transferring activities. Sometimes an activity gets corrupted (not showing complete data in the activities history on the watch), and once I delete the corrupted activity, it works fine again. If the corrupted activity isn't deleted, it sometimes keeps trying to transfer, and keeps failing. If I put it on the charger in this state, it will loose charge and continue to vibrate occassionally - possibly the "reverse charging" issue that some people have experienced. Recently, it hung up while I was resetting an activity, and that activity got corrupted during vibrating reset signal. It didn't stop vibrating until I turned the watch off. Then I had to sleep my computer to get it to stop trying to transfer the corrupted activity before I could fix the problem. Another time, I had to do a complete reset to fix the watch (special sequence of button pushes - look it up on Garmin), which reset the watch to the out of the box condition (deleting waypoints, HR settings, etc.). I think I can avoid that now that I'm familiar with how the watch gets hung up.
The running dynamics metrics features on the 620 seem almost entirely useless to me. My cadence is fine, though I can see it maybe being useful for beginners with really bad form. I don't see the vertical oscillation and ground contact times as being useful for training. Bounciness of a stride can be often be a good thing, indicating good springiness, and I can see people messing up their from trying to minimize vertical oscillation when they shouldn't. There's a lot of variation in ground contact time among even the elites going the same pace, so what are you supposed to try to do with that data?
The main pluses of the 620 to me might be the longer battery life and the better strap attachment. Slimmer and lighter is nice, but the 610 isn't that thick or heavy. I don't have a smartphone so the bluetooth link is useless for me. The Wifi sounds good, but I wonder if it would have the same issues with incompete data transfer that the 610 does. Also the online training log that I use does Garmin transfers from a folder on my computer, not from Garmin Connect, so I would probably have to use to cable for the transfers to my computer first, unless I'm missing something about how that works.
The on the Garmin 620 forum, there are complaints about GPS accuracy, so it might be good to wait until they update the firmware a few times before buying.