Perhaps it could work with a button to inquiry the internet if all you have is "up to speed"? Most people wouldn't mind some minutes of machine-thinking if that means it can assess correctly what you are missing, what you are not missing, what is corrupted, etc.
For instance, it's glaringly ugly for me to run the application and it implicitly telling me I haven't download the mediavps, but that I did download Sync, when I just downloaded the former months ago and used the app to download the latter.
Hmm. This is a reasonable thing to add. I'll look into it.
Yet it seems to take rather long and consume significant amounts of bandwith. Wouldn't putting this information in a seperate .txt file be a lot faster?
It might be faster but it would require the mod maker to keep the text file up to date. That's an extremely brittle system. No, it's better to scan from the archive, which is the same place the files will actually be extracted from. Also, see the next point.
The installer doesn't actually download the files to check the size, it merely checks the size HTTP reports.
This is not quite correct. For archives, the installer seeks to the archive's table of contents and then examines the sizes listed there. This requires scanning through the archive over HTTP, so you could think of it as "downloading" even though nothing is extracted and nothing is saved to your computer.
The ideal way to get the contents is not to stream the entire archive but rather seek to the proper position. But this requires some gymnastics with the HTTP connection that I haven't investigated due to more pressing development needs on the installer. See
this thread on HLP and
this thread on the 7zip-JBinding forum where I discussed the problem more extensively.
Regardless, the issue I first made a report about has been fixed: The FSOpen installer seems to properly recognize that the MVP2014s download has failed, and therefore I don't need to check the re-run installation button to ensure that everything works.
I shall now see if I can get the other files.
Good.

User reports selecting 'complete' but looks like they did not get MVPs 3.6.12.
I'll check. I've responded on the other thread.