I think some of the leaks have said 4.6". I know it seems small but a 10th of an inch can make a difference
Yeah, 1080p on a 5" screen is really questionable. 300dpi makes things smooth but 440dpi is just rediculas. You won't notice the difference but it will cost battery and performance to have that extra-high resolution. I am also afraid that HTC will not give it a large enough battery. HTC makes great phones but many of their's have had batteries that were too small. The original Evo and Droid Inc are great examples. Terrible battery life on both - it's like they were not tested. Those two were a huge reason Android got a big black eye when it comes to battery life early on.
With the One series and the 28nm S4 chipsets with integrated LTE things have changed a little and an 1800mAH battery should be enough to easily get through a day. It still doesn't compete, in my opinion, with Moto taking things to the next level by using a 3300mAH battery. When moto releases a S4 based phone with a 3300mAH battery you'll be looking at significantly better battery life than the Maxx. That will probably be the Razr HD. I can't wait!