Please notice on linux version 4.3.3 I had no problems, and now with version 4.4.1 the problems are there.

The problems are present both on plain terminal (no Xorg) or under X (Xorg).

I'm not setting any particular mode setting, and I just let KMS do its magic.  On X, I have no configuration for the graphics at all, letting again KMS and Xorg do their magic.

I'm using i915 driver, on a MintBox 2 Arch gnu/linux box, which comes with a "Intel HD Graphics 4000", which according to lspci -v:

00:02.0 VGA compatible controller: Intel Corporation 3rd Gen Core processor Graphics Controller (rev 09) (prog-if 00 [VGA controller])
Subsystem: Intel Corporation Device 2211
Flags: bus master, fast devsel, latency 0, IRQ 28
Memory at e0000000 (64-bit, non-prefetchable) [size=4M]
Memory at c0000000 (64-bit, prefetchable) [size=512M]
I/O ports at 4000 [size=64]
Expansion ROM at <unassigned> [disabled]
Capabilities: [90] MSI: Enable+ Count=1/1 Maskable- 64bit-
Capabilities: [d0] Power Management version 2
Capabilities: [a4] PCI Advanced Features
Kernel driver in use: i915
Kernel modules: i915

I don't have any particular modprobe setting for the i915 module, just default.

Another important piece of information prior to describe the problems, is that the display is hooked to the box through its HDMI port.

Now the problems...

1.-  Resolution problem @ boot
     =========================

If the box boots before the display has turned on and is waiting for signal on the hdmi port, then the 2 never get to negotiate the right resolution and a pretty low one gets picked.  The display has some manual setting, but the "native" one from what it's hooked to is not an option, like there's no way for the display to negotiate with the box...  BTW, the display is a 720p one...

To keep things totally automatic, the only work around is to turn the display on, until its state of waiting for signal on the hdmi port, and then turn the box on.  If this is missed, a reboot is required to get the box and the display to negotiate the resolution.

2.-  Resolution problem @ non fully asleep power saving state
     ========================================================

When left turned on, but unused, at some point the box graphics get to a state such that it blanks the display, but it's not totally asleep.  At that point one can turn the display back on, but the same resolution problem as the boot one shows up.  If leaving everything automatic, a reboot is required.

3.-  Graphics never recovering from fully asleep power saving state
     ==============================================================

When left turned on, but unused, at some point the box graphics get to a state such that it blanks the display and the graphics get totally asleep.  At that point, one can turn the display on, then off, then on again and so on, that the graphics never wake up.  At that point, if not handled remotely, the option is a hard power button (whether it turns off or reboot the box is a matter of configuration).

To prevent getting into this state under Xorg, I'm using as a work around:

xset s off
xset -dpms