I'm getting a bug where when I order units to move and orient them, the arrow and unit circles tend to get obscured by uneven terrain (everything shows up fine when moving sea units).

Anyone know how to fix that?

If it helps, the game is the Gold Edition, no mods or patches.

I assume we're speaking about the first game in the series.
I have the same bug on Windows 10, couldn't make it disappear, although I didn't put too much effort into it except the usual Windows compatibility settings. Seeing some gameplay videos the problem could be solved with mods, though. The two most mentioned ones are https://www.neoee.net and https://empireearth.eu/drexmod. Both of those touch gameplay, visual and multiplayer aspects of the game. Didn't try them out yet, wanted to fiddle with the game a bit more to get the vanilla experience first.
Another interesting bit of information is that on Linux (Debian) the game doesn't produce this bug, so it's not hard-baked into the code neither by the developers nor by the GOG team. It produces other problems, though, so it's not the best experience here, either.

I see, thanks.