Recently we had to setup the Google Apps (Google Mail) for a client with One.com hosting company. Everything was same but MX entry for Mail DNS server was not as advised by Google or as per other hosts.
It is always suggested to add .(period) in the end of host entry like: aspmx.l.google.com. Notice the ". " in the end of the above host address but ONE.com hosting will not accept it, they will simply empty the records and will not show any error or whatsoever.
So for ONE.com hosting clients it is recommended to use Host names without PERIOD at the end so that your entries will look like this:
Notice there are no PERIODS at the end of Server entries.