We just had the same problem with some clients, and after some digging it had something to do with the Spring 17 release.
The easy way to fix it is by clearing your local files. In chrome you can do this by following these steps:
- Open the page that doesn't show the picklist values
- Open Developer Tools (F12, or right mouse button somewhere in the page -> inspect element)
- Go to the Network tab
- On the top check the "Disable cache" checkbox
- Reload your page
- Uncheck the "Disable cache"
- Close developer tools
If a Salesforce developer reads this: