Edit: Just going ahead and restarting the download.
If I get an checksum error with the downloader, is there really any other option than redownloading it?
A checksum is a mathematically unique hash code for a file generated from the contents of the file and designed so that the slightest difference in the file, such as one bit being flipped from on to off or vice versa will result in a huge difference in the checksum which then indicates that the file is corrupted somehow.
So, if you get a checksum error (with anything that uses checksums not just GOG downloader), this indicates the file is corrupted. That could be because it was corrupted transferring over the Internet to your computer, having damaged computer memory or hard disk sectors which corrupt the file, or it could be due to software corruption such as a buggy driver scribbling all over memory in the system corrupting random data, could be due to system overheating some component in the computer or other factors. In any case, a bad checksum indicates the file as the software (GOG downloader) sees it, does not match the file stored on GOG's servers and either the file or the checksum itself got corrupted somewhere along the way.
Knowing how that works, the only option is to obtain an uncorrupted copy of the file to replace the corrupted one. That will generally mean downloading it, or breaking into GOG offices in the middle of the night and copying it onto a memory stick. :) There isn't really any other option to fix a corrupted file other than to obtain it uncorrupted again somehow and the two options are GOG downloader or direct HTTP downloads. Having said that, if you don't know how or why the download got corrupted in the first place, it could just as easily get corrupted the second time you try to download it as well. In either case, if it tells you the checksum doesn't match it is detecting that corruption occurred somewhere along the line.
Hope this helps.