A reduced test case for the issues with <lightning:input /> bindings

lightningInputRepro.cmp

<aura:component implements="force:appHostable">

  <!-- public attributes -->
  <aura:attribute name="myObj" type="Account" default="{Name: '', Type: ''}" access="PUBLIC" />

  <!-- body markup -->
  <c:lightningInputReproFields record="{!v.myObj}" />
  <lightning:button label="Update Object" onclick="{!c.updateObj}" />
  <lightning:button label="Update Name" onclick="{!c.updateName}" />

</aura:component>

lightningInputReproController.js

({
  updateObj: function (component, event, helper) {
    var rand = Math.floor(Math.random() * 99);
    var newObj = {
      'Name': 'new name ' + rand,
      'Type': 'new type ' + rand
    };
    component.set('v.myObj', newObj);
  },
  updateName: function (component, event, helper) {
    var rand = Math.floor(Math.random() * 99);
    component.set('v.myObj.Name', 'new name ' + rand);
  }
})

lightningInputReproFields.cmp

<aura:component >

  <!-- public attributes -->
  <aura:attribute name="record" type="Account" default="{Name: '', Type: ''}" access="PUBLIC" />

  <!-- body markup -->
  <lightning:input name="name" type="text" label="Name" value="{!v.record.Name}" />
  <lightning:input name="type" type="text" label="Type" value="{!v.record.Type}" />

</aura:component>