So far I'm getting these issues, most of them occur randomly in Remastered view, but some in both:
* characters or background flicker with black boxes (Remastered only)
* background or the whole screen goes black (only subtitles stay visible) (Remastered only)
* random crashes at various points of the game, usually related to cutscenes (one particular crash appeared almost every time, before the cutscene where Cavefish rush after you when you steal the ramp) (both versions)

I wasn't able to get a stable solution, and made some random manipulations:
* disable cloud
* disable overlay
* force 640x480 resolution
* change graphics settings
* turn fullscreen on/off
* game restart

Since most of these issues appear randomly, sometimes it helped.

I'm running Windows 7 x64 with Intel HD Graphics 4000. From time to time I have issues with Intel HD Graphics, but since it is explicitly listed in the list of supported GPUs, I expect at least to play a game without crashes.

Running with Windows 7 64 bit with no problems whatsoever. So it is not a OS problem.
I suggest you email GOG support about this. You will get faster help then just posting about it.
And I suggest you invest in a dedicated Nivida or ATI video card. THe Intel video chips are notorious for being crappy for gaming. Even games that support it often have pisspoor performance on the Intel chips.