When trying to emulate the looks and feel of retro game systems there isn't much room for interpretation regarding the system's specific limitations. Sometimes it's easy to get the specifics wrong, though. This shall be a place to discuss them.
Taking the ZX Spectrum, it's clear that it has a limited color palette of which it can only ever display two colors per 8x8 pixel attribute. What about scrolling, though?
There's a video showcasing parallax scrolling:
You'd probably not remember this feature fondly from the olden days, though.
Lots of games scrolled per tile, some managed to have smooth per-pixel scrolling, though what'd
feel the most authentic? In this particular case, the limitation of attribute clash would be a good pointer.
Because every 8x8 pixel tile can only ever have two colors, you can't scroll anything on a per-pixel basis unless everything you're scrolling has the same two colors:
Otherwise you'd be looking at a hell of attribute-clash. So you could have both per-pixel or per-tile scrolling, with the less limited option introducing another limit, keeping look and feel authentic in both cases.
In this example, the limitations are broken in a lot of ways. The background and tower should scroll at intervals of 8 pixels, to avoid ending up with attributes that are holding more than 2 colors for some of the frames. What about the background scrolling in one and the tower in the other direction at different speeds, though? Honestly, I don't know exactly.
Systems can always be pushed to new heights, but if you're not actually developing for them, which in most cases might be the more realizable way to go about things, not overstepping the threshold becomes the challenge. I'm just dealing with ZX Spectrum stuff at the moment, but feel free to talk about any system you'd like.