The info in my library states the the file size for Windows Installer, English (part 1 of 2) should be 1.3 GB, yet the downloaded file is only 30.1 MB in size. Below are screenshots of the library, a partial screenshot from Firefox's downloads tab, and a partial one from my file manager.

Is that an error in the library, i.e. wrong info, or is there a problem with the file?

There should be a problem with the downloaded file, it's definitely not that small. If you downloaded the file using the direct link, try re-downloading via GOG Downloader, or the other way around, if you downloaded via Downloader, as it often solves things.

If none of this works, try refreshing your account and trying again, or you can always contact GOG Support as a last resort.

It looks like the file actually is that small. I've downloaded it multiple times now via browser and GOG Downloader, and the file size remains the same. The game installed successfully and appears to be working (I've only watched the intro sequence so far), so it's most likely just a case of wrong information shown in the game library.

A mistake on GOG part, the file size should actually be 30MB.

http://www.gog.com/forum/broken_sword_series/a_big_question

In the 2.0 version the first file was 1.3 GB and the other files were language-packs (each ~400 MB).
Since GOG updated to version 2.1 the first file is 30 MB and the language-packs and the main file are merged into the 2.7 GB file but they forgot to change the information about the filesize for the first file.

HTH