If you create a global parameter with a period character, you are then unable to modify or delete it.
I haven't tested this with host-group or host-level parameters, but I suspect the behaviour will be the same.

For example, I created a global param called "net.ifnames". When I try to edit it:

Started GET "/common_parameters/net.ifnames/edit" for 10.x.x.x at 2015-07-28 10:16:30 +0100
2015-07-28 10:16:30 [F]
ActionController::RoutingError (No route matches [GET] "/common_parameters/net.ifnames/edit"):
/usr/share/gems/gems/passenger-4.0.18/lib/phusion_passenger/rack/thread_handler_extension.rb:77:in `process_request'
/usr/share/gems/gems/passenger-4.0.18/lib/phusion_passenger/request_handler/thread_handler.rb:140:in `accept_and_process_next_request'
/usr/share/gems/gems/passenger-4.0.18/lib/phusion_passenger/request_handler/thread_handler.rb:108:in `main_loop'
/usr/share/gems/gems/passenger-4.0.18/lib/phusion_passenger/request_handler.rb:441:in `block (3 levels) in start_threads'

Trying to delete it:
Started DELETE "/common_parameters/net.ifnames" for 10.x.x.x at 2015-07-28 10:17:06 +0100
2015-07-28 10:17:06 [I] Processing by CommonParametersController#destroy as
2015-07-28 10:17:06 [I] Parameters: {"authenticity_token"=>"xxxx", "id"=>"net"}
2015-07-28 10:17:06 [I] Completed 406 Not Acceptable in 7ms (ActiveRecord: 1.1ms)
2015-07-28 10:17:21 [I]

I guess either the validation should be changed to prevent me from creating a variable with a period char in it, or the backend needs to handle params with a period in the name.