How to detect modules enabled incorrectly?
The problem is that it depends on each module. When enabled, a module sets up its environment (create tables, variables, declare URL, etc) but this environment is not declared explicitly so you can't automatically check that the module has been installed correctly.

You may check the install file for the modules's scheme (tables defined by the module) and the hook_enable to see what tasks needs the module when is enabled.

I think best way is to uninstall modules and try to install them again, so all modules's environent are cleared when unisntalling and set up again when enabled again.

Using drush this tasks is very easy and handy.

Ah, and try to clear caches to see if modules works, but you won't be sure modules installed correctly...