It's not just the constants mod, there was an issue with packing the files for the 1.0 release which will break the mod system for all mods. It will probably be fixed within a day.
Viewing post in Constants mod not functioning
This topic was related to problems specific to version 1.0. Version 1.0a fixed those problems. If you have 1.0, then please get the current version. There are current no errors for constants mod in vanilla 1.0a, so if you have problems you will need to post the error messages for me to figure out what happened. Either screenshot the errors or type them here.