If a scenario has been unlocked and then mods are added to the server that have parts from those scenarios then they cannot be unlocked. E.g:
Kerbal Engineer Redux adds parts to the start scenario.
When you attempt to unlock these parts clicking on them brings up the Research part and clicking research shows them as being unlocked.
Going to the VAB shows the parts as needing to be unlcoked despite the fact the already have been and going back to the R&D center shows them as being locked again.

This one feels like it's not actually a DMP bug. Can you reproduce this in single player doing the same thing?

I have played career and not had this issue. Can you put a copy of your server up on dropbox or something so I can have a look at it?

It doesn't happen in single player which is why it seems likely it was a server bug, here's a dropbox link to the server: https://www.dropbox.com/s/4i9k6njut5eqdtu/DMPServer.zip

I tried again and couldn't recreate this bug. The server looks fine. (Sorry for the late response). Are you using any sort of tech tree mods? Apparently some of those cause issues, I've seen.

The only mods on there are Kerbal Engineer Redux and ProceduralFairings which do add things to the tech tree. The problem can be fixed if I add the parts to the players scenario file, so what appears to be happening is that once you've unlocked a node on the tech tree if mods are added that add to the unlocked node, you can't unlock those parts as it doesn't save them to the scenario file.

If this still happens, then it's not possible to solve. Instead of loading the scenario module now, DMP adds them to a list during the game start instead of starting the game and then loading the modules.