Expect possible reception issues. My Thunderbolt and Bionic work in more places than my S4, and pull stonger signals than the S4. I often have places where the S4's signal strength meter shows 'bars" but I have no data, and sometime can't even make a call. These are places where my TB and Bionic work. While the S4 shows "2 bars" its signal is -102 or -103db. Every phone I've had stops working at -105db. This ME7 update has included new radio code, but hasn't improved reception for me. When I look back at all my "Dumb", "Feature" and "Smart" phones, with rare exception (like the U620) Samsung has always been at the back of the pack for reception. This hasn't changed in the 20 years since I got my first Audiovox Bag phone. Its unfortunate due to the many great features of their phones.
My S4 does get HOT up around the camera while on phone calls, charging, or using data a lot. I can feel it on the back side of the device when not using a case. Where I put my hand while holding it normally, its just very warm. If I consciously put my hand in that spot on the back, yes its way hotter than any other phone I have, and I can feel it immediately when I put the phone back in my pants pocket. When its hot like this, the screen over that spot is warm, but not uncomfortable. It has not got to the point where the phone reboots, shuts down, or otherwise stops working or performing a function due to the heat, so I'm thinking its "normal" that this phone just runs hotter than every other phone I have. With a case, I can't feel it on the back much.
Consider getting a 32gig version of the phone, or don't expect to put bigger apps/games on the phone due to it available memory and internal storage. I haven't wiped after the latest upgrade, but out of the box, my 16gig device had 8.5gig free. Pin some offline music in Google Plus or download some tunes in Rhapsody, and that gets eaten up quick. Download a game like Asphalt 7 (which takes up 1.3gig), and you're left with nothing. The latest update's Apps2SD support doesn't help much to alleviate this issue. While it can move the APP to SD, it often can't move the APP DATA which is the bigger part. (1.2gig of Asphalt 7's data stays internal when "moving to SD").
Forget about rooting, S-OFF, etc. The latest S4 software update closed the loop hole used for Root. Anyone who was rooted and took the update lost root with (at this point) no way to get it back. This didn't impact just the Verizon S4, but ATT and Sprint as well. Samsung is pushing their KNOX security as a feature to corporate/enterprise customers, its included in the latest update, and its likely the issue here.
Due to its size and lack of bezel, especially along the bottom, be prepared to re-learn how to hold the device, re-position it in your hand when needed (like trying to get your thumb up to the top of the screen then need to hit the buttons at the bottom), etc. The volume controls on the "other side" will also take getting used to. The power button on the S4 is right where my thumb is when holding the phone in a way that feels natural to me. I have to adjust how I hold it. I often feel like I'm going to drop the S4 when I have to re-position it to get between the top and bottom of the screen, and often hit the back or home button when trying to catch it. My hands are average size for someone who is 6' 1" Some previous Samsung users might not have these issues with holding, and operating the S4. I guess it can be kind of equated driving a chevy and getting into a ford, the controls, blind spots, etc take some getting used to.
Some of my previously purchased games do not install, or work. EA's Need for Speed, Tiger Woods PGA Tour 12, Madden NFL 12, Mass Effect Infiltrator, Real Racing 2, Gameloft's Uno (w/Friends works, local only version installs but errors its not compatible when it tries to download extra files), Jeopardy! HD by Sony Pictures Television, Monopoly by Electronic Arts Inc (classic monopoly, not millionaire, or hotels, which I haven't tried), are just a few that I've tried to install/play which either don't work, or give and error when I launch them they are not compatible.
Screen is nice. Its bright and easy to read. The phone doesn't lag, but I've turned off many/most of the extra features. Camera quality is very nice. The battery lasts through lasts a little longer than a day. Having removable battery and MicroSD slot is nice, but the limits of not being able to move apps/data to it gets in the way a little. Thankfully, the camera app does store its pix on the microSD, so you can take more, as well as take longer videos.
The S4 also has a lot of features. Many that I don't make use of.
I do find it odd that the physical home button powers the screen on, especially since that button is more raised or flush than recessed, and can be hit when the phone is put in a pocket. Yes, with the screen on, it does generate heat which can be felt by my leg.
As for being fragile, or screen breakage, from what I've been reading, it appears some have put their phone in their pocket, etc, and later found the screen cracked. Ok, with a plastic frame, very little bezels around it, the stiffest part is the front glass, so yeah, I could understand the frame flexing a little under stress, and I could see that leading to the screen inside to crack. If you wear very loose pants, don't put it on your pocket, don't sit with it in your pocket or have a rigid case on it to provide extra support, I think you could reduce your risks. I'm using the shell/holster combo case from Verizon, even though I'm not using the holster part, unless I plan to through the phone in my back pack. The part that covers the back of the phone is thin, light, doesn't add bulk to the phone, yet adds stiffness and support to it.
Some of the negatives I've mentioned, I could overcome them in time and adjusting my usage habits. The only major sticking point to me is the reception issue.
EDIT: updates since I initially wrote this...
1. Monopoly from the Amazon App Store does work, where as the one from Google Play still doesn't work. None of the others have started working since the ME7 Update.
2. A Root process for the ME7 update has been posted, however this process only allows for Root. It does not allow for flashing custom roms. The Bounty for finding a way to unlock the boot loader still stands. Not sure if they will ever find a way, but I hope so. And the next ROM update from Verizon might close this loophole now used for rooting. If you want to root and flash custom roms, your best bet is the Developer Edition direct from Samsung with only 16gig and a short warranty (like 30 days) that is voided as soon as you flash a custom rom.