Orange check means that the level has changed. If I remember correctly, it uses the CRC32 of the level file to detect this, so this should only happen if the file has actually changed. EDIT: Just tested, it apepars it actually uses the modified date. Thus, if you use the installer when upgrading, it will likely overwrite existing files with new copies, which will turn the checkmarks orange even if the level itself hasn't changed at all. However, if you have your replay files (assuming you haven't disabled it, NeoLemmix should automatically be saving them in replay/[game name]/Auto), you can run a replay mass check on them; this will restore the green checkmarks (as long as your replay still solves the level).

The NeoLemmix styles download at one point had corrupted versions of the LPVI styles; redownloading the styles should fix this.

Well most of the checkmarks (which there are a lot of) are orange now and I definitely haven't manually updated NeoLemmix in a long time. (Would it be best to use an attached update to do that or use the installer?) Also, unfortunately I haven't been saving any replays. But as long as the checkmarks are still there at all (regardless of color) then I suppose I could be much worse off.

In any case Lemmings Plus VI works correctly now so thank you for that at least.

The installer will also get the latest version of all the included-by-default level packs, so that might be nice. But ultimately, all the installer does is download the ZIP files and extract them to the correct places, so it makes little difference. You may want to consider downloading manually if you're on an internet plan with a low data cap (eg. a cellphone hotspot), as some of the downloaded by default packs have a lot of large music files. (NepsterLems, Lemmings Reunion and Lemmings Plus VI are the biggest offenders here.)