After Square's early success in mobile payments, rivals latched on to the question of its security. But after Square put most of those concerns to rest, in part by tightening up its approach to security, competitors have changed tactics to focus on Square's customer support.

In recent months, big names such as PayPal (s ebay) , VeriFone (s pay), NCR (s ncr), Groupon (s grpn) and smaller competitors such as PayAnywhere have…